This HP 12C Platinum Owner’s Handbook and Problem-Solving Guide is
intended to help you get the most out of your investment in your HP 12C
Platinum Programmable Financial Calculator. Although the excitement of
acquiring this powerful financial tool may prompt you to set this handbook aside
and immediately begin “pressing buttons,” in the long run you’ll profit by
reading through this handbook and working through the examples it contains.
Following this introduction is a brief section called Making Financial
Calculations Easy—which shows you that your HP 12C Platinum does just that!
The remainder of this handbook is organized basically into three parts:
z Part I (sections 1 through 7) describes how to use the various financial,
mathematics, statistics, and other functions (except for programming)
provided in the calculator:
z Section 1 is about Getting Started. It tells you how to use the keyboard,
how to do simple arithmetic calculations and chain calculations, and
how to use the storage registers (“memories”).
z Section 2 tells you how to use the percentage and calendar functions.
z Section 3 tells you how to use the simple interest, compound interest,
and amortization functions.
z Section 4 tells you how to do discounted cash flow analysis, bond, and
depreciation calculations.
z Section 5 tells you about miscellaneous operating features such as
Continuous Memory, the display, and special function keys.
z Sections 6 and 7 tell you how to use the statistics, mathematics, and
number-alteration functions.
z Part II (sections 8 through 11) describe how to use the powerful
programming capabilities of the HP 12C Platinum.
z Part III (sections 12 through 16) give you step-by-step solutions to
specialized problems in real estate, lending, savings, investment analysis,
and bonds. Some of these solutions can be done manually, while others
involve running a program. Since the programmed solutions are both selfcontained and step-by-step, you can easily employ them even if you don’t
care to learn how to create your own programs. But if you do start to create
your own programs, look over the programs used in the solutions: they
contain examples of good programming techniques and practices.
2
Introduction3
z The various appendices describe additional details of calculator operation
as well as warranty and service information.
z The Function Key Index and Programming Key Index at the back of the
handbook can be used as a handy page reference to the comprehensive
information inside the manual
Financial Calculations in the United Kingdom
The calculations for most financial problems in the United Kingdom are
identical to the calculations for those problems in the United States – which are
described in this handbook. Certain problems, however, require different
calculation methods in the United Kingdom than in the United States. Refer to
Appendix G for more information.
For More Solutions to Financial Problems
In addition to the specialized solutions found in Sections 12 through 16 of this
handbook, many more are available in the optional HP 12C Platinum Solutions Handbook. Included are solutions to problems in lending, forecasting, pricing,
statistics, savings, investment analysis, personal finance, securities, Canadian
mortgages, learning curves in manufacturing, and queuing theory. The solutions
handbook is available from your authorized HP dealer.
Bond Calculations....................................................................................... 204
Function Key Index ..................................................................... 205
Programming Key Index ............................................................. 208
Subject Index ............................................................................... 211
Making Financial
Calculations Easy
Before you begin to read through this handbook, let’s take a look at how easy
financial calculations can be with your HP 12C Platinum. While working
through the examples below, don’t be concerned about learning how to use the
calculator; we’ll cover that thoroughly beginning with Section 1.
Example 1: Suppose you want to ensure that you can finance your daughter’s
college education 14 years from today. You expect that the cost will be about
$6,000 a year ($500 a month) for 4 years. Assume she will withdraw $500 at the
beginning of each month from a savings account. How much would you have to
deposit into the account when she enters college if the account pays 6% annual
interest compounded monthly?
This is an example of a compound interest calculation. All such problems
involve at least three of the following quantities:
z n: the number of compounding periods.
z i: the interest rate per compounding period.
z P
W
: the present value of a compounded amount.
z PMT: the periodic payment amount.
z FV: the future value of a compounded amount.
In this particular example:
z n is 4 years × 12 periods per year = 48 periods.
z i is 6% per year ÷ 12 periods per year = 0.5% per period.
z PV is the quantity to be calculated – the present value when the financial
transaction begins.
z PMT is $500.
z FV is zero, since by the time your daughter graduates she (hopefully!) will
not need any more money.
To begin, turn the calculator on by pressing the ; key. Then, press the keys
shown in the Keystrokes column below.
Note: A battery symbol () shown in the upper-left corner of the
display when the calculator is on signifies that the available battery power
is nearly exhausted. To install new batteries, refer to Appendix F.
1
1.
If you are not familiar with the use of an HP calculator keyboard, refer to the description
on pages 16 and 17.
11
12 Making Financial Calculations Easy
The calendar functions and nearly all of the financial functions take some
time to produce an answer. (This is typically just a few seconds, but the
¼, !, L, and S functions could require a half-minute or more.)
During these calculations, the word running flashes in the display to let
you know that the calculator is running.
KeystrokesDisplay
fCLEARHf2
4gA
6gC
500P
g×
$
aDon’t be concerned now about the minus sign in the display. That and other details will
be explained in Section 3.
Example 2: We now need to determine how to accumulate the required deposit
by the time your daughter enters college 14 years from now. Let’s say that she
has a paid-up $5,000 insurance policy that pays 5.35% annually, compounded
semiannually. How much would it be worth by the time she enters college?
In this example, we need to calculate FV, the future value.
0.00
48.00
0.50
500.00
500.00
–21,396.61
Clears previous data inside the
calculator and sets display to show
two decimal places.
Calculates and stores the number of
compounding periods.
Calculates and stores the periodic
interest rate.
Stores periodic payment amount.
Sets payment mode to Begin.
Amount required to be deposited.
a
Keystrokes (RPN mode) Display
fCLEARG
14\2§w
5.35\2z¼
5000Þ$
M
Example 3: The preceding example showed that the insurance policy will
provide about half the required amount. An additional amount must be set aside
to provide the balance (21,396.61 – 10,470.85 = 10,925.76). Suppose you make
monthly payments, beginning at the end of next month, into an account that pays
–21,396.61
28.00
2.68
–5000.00
10,470.85
Clears previous financial data
inside the calculator.
Calculates and stores the number of
compounding periods.
Calculates and stores the periodic
interest rate.
Stores the present value of the
policy.
Value of policy in 14 years.
Making Financial Calculations Easy13
6% annually, compounded monthly. What payment amount would be required in
order to accumulate $10,925.75 in the 14 years remaining?
KeystrokesDisplay
fCLEARG
14gA
6gC
10925.76M
gÂ
P
Example 4: Suppose you cannot find a bank that currently offers an account
with 6% annual interest compounded monthly, but you can afford to make
$45.00 monthly payments. What is the minimum interest rate that will enable
you to accumulate the required amount?
In this problem, we do not need to clear the previous financial data inside the
calculator, since most of it is unchanged from the preceding example.
10,470.85
168.00
0.50
10.925.76
10.925.76
–41.65
Clears previous financial data
inside the calculator.
Calculates and stores the number of
compounding periods.
Calculates and stores the periodic
interest rate.
Stores the future value required.
Sets payment mode to End.
Monthly payment required.
KeystrokesDisplay
45ÞP
¼
12§
This is only a small sampling of the many financial calculations that can now be
done easily with your HP 12C Platinum. To begin learning about this powerful
financial tool, just turn the page.
–45.00
0.42
5.01
Stores payment amount.
Periodic interest rate.
Annual interest rate.
Part I
Problem Solving
Section 1
Getting Started
Power On and Off
To begin using your HP 12C Platinum, press the ; key1. Pressing ; again
turns the calculator off. If not manually turned off, the calculator will turn off
automatically 8 to 17 minutes after it was last used.
Low-Power Indication
A battery symbol () shown in the upper-left corner of the display when the
calculator is on signifies that the available battery power is nearly exhausted. To
replace the batteries, refer to Appendix F.
The Keyboard
Many keys on the HP 12C Platinum perform two or even three functions. The
primary function of a key is indicated by the characters printed in white on the
upper face of the key. The alternate function(s) of a key are indicated by the
characters printed in gold above the key and the characters printed in blue on the
lower face of the key. These alternate functions are specified by pressing the
appropriate prefix key before the function key.
:
z To specify the alternate function printed in
gold above a key, press the gold prefix key
(f), then press the function key.
z To specify the primary function printed on
the upper face of a key, press the key alone.
z To specify the alternate function printed in
blue on the lower face of a key, press the
blue prefix key (g), then press the
function key.
Throughout this handbook, references to the operation of an alternate function
appear as only the function name in a box (for example, “The L function …”).
References to the selection of an alternate function appear preceded by the
1.
Note that the ; key is lower than the other keys to help prevent its being pressed
inadvertently.
16
Section 1: Getting Started17
appropriate prefix key (for example, “Pressing fL …”). References to the
functions shown on the keyboard in gold under the bracket labeled “CLEAR”
appear throughout this handbook preceded by the word “CLEAR” (for example,
“The CLEAR H function …” or “Pressing fCLEARH …”).
If you press the f or g prefix key mistakenly, you can cancel it by pressing
fCLEAR X. This can also be pressed to cancel the ?, :, and i
keys. (These keys are “prefix” keys in the sense that other keys must be pressed
after them in order to execute the corresponding function.) Since the X key is
also used to display the mantissa (all 10 digits) of a displayed number, the
mantissa of the number in the display will appear for a moment after the X
key is released.
Pressing the f or g prefix key turns on the corresponding status indicator – f
or g – in the display. Each indicator turns off when you press a function key
(executing an alternate function of that key), another prefix key, or
fCLEAR X.
Keying in Numbers
To key a number into the calculator, press the digit keys in sequence, just as if
you were writing the number on paper. A decimal point must be keyed in (using
the decimal point key) if it is part of the number unless it appears to the right of
the last digit.
Digit Separators
As a number is keyed in, each group of three digits to the left of the decimal
point is automatically separated in the display. When the calculator is first turned
on after coming from the factory – or after Continuous Memory is reset – the
decimal point in displayed numbers is a dot, and the separator between each
group of three digits is a comma. If you wish, you can set the calculator to
display a comma for the decimal point and a dot for the three-digit separator. To
do so, turn the calculator off, then press and hold down the . key while you
press ;. Doing so again sets the calculator to use the original digit separators
in the display.
Negative Numbers
To make a displayed number negative – either one that has just been keyed in or
one that has resulted from a calculation – simply press Þ (change sign). When
the display shows a negative number – that is, the number is preceded by a minus
sign – pressing Þ removes the minus sign from the display, making the
number positive.
18 Section 1: Getting Started
Keying in Large Numbers
Since the display cannot show more than 10 digits of a number, numbers greater
than 9,999,999,999 cannot be entered into the display by keying in all the digits
in the number. However, such numbers can be easily entered into the display if
the number is expressed in a mathematical shorthand called “scientific notation.”
To convert a number into scientific notation, move the decimal point until there
is only one digit (a nonzero digit) to its left. The resulting number is called the
“mantissa” of the original number, and the number of decimal places you moved
the decimal point is called the “exponent” of the original number. If you moved
the decimal point to the left, the exponent is positive; if you moved the decimal
point to the right (this would occur for numbers less than one), the exponent is
negative. To key the number into the display, simply key in the mantissa, press
Æ (enter exponent), then key in the exponent. If the exponent is negative,
press Þ after pressing Æ.
For example, to key in $1,781,400,000,000, we move the decimal point 12
places to the left, giving a mantissa of 1.7814 and an exponent of 12:
KeystrokesDisplay
1.7814Æ12
Numbers entered in scientific notation can be used in calculations just like any
other number.
1.781412
1,781,400,000,000 entered in
scientific notation.
The CLEAR Keys
Clearing a register or the display replaces the number in it with zero. Clearing
program memory replaces the instructions there with gi000. There are
several clearing operations on the HP 12C Platinum, as shown in the table
below:
Key(s)Clears:
ODisplay and X-register.
fCLEAR²Statistics registers (R
The calculator can be set to perform arithmetic operations in either RPN
(Reverse Polish Notation) or ALG (Algebraic) mode.
In reverse polish notation (RPN) mode, the intermediate results of calculations
are stored automatically, hence you do not have to use parentheses.
In algebraic (ALG) mode, you perform addition, subtraction, multiplication, and
division in the traditional way.
To select RPN mode: Press f] to set the calculator to RPN mode. When the
calculator is in RPN mode, the RPN status indicator is lit.
To select ALG mode: Press f[ to set the calculator to ALG mode. When
the calculator is in ALG mode, the ALG status indicator is lit.
Example
Suppose you want to calculate 1 + 2 = 3.
In RPN mode, you enter the first number, press the \ key, enter the second
number, and finally press the arithmetic operator key: +.
In ALG mode, you enter the first number, press +, enter the second number,
and finally press the equals key: }.
RPN modeALG mode
1 \ 2 +1 + 2 }
In RPN mode and algebraic mode, the results of all calculations are listed.
However, in RPN mode only the results are listed, not the calculations.
Most examples in this manual (except those in Appendix B) assume that RPN
mode is selected. Some examples will also be correct if you are in ALG mode.
Simple Arithmetic Calculations in RPN Mode
In RPN mode, any simple arithmetic calculation involves two numbers and an
operation – addition, subtraction, multiplication, or division. To do such a
calculation on your HP 12C Platinum, you first tell the calculator the two
numbers, then tell the calculator the operation to be performed. The answer is
calculated when the operation key (+,-,§, or z) is pressed.
The two numbers should be keyed into the calculator in the order they would
appear if the calculation were written down on paper left-to-right. After keying
in the first number, press the \ key to tell the calculator that you have
completed entering the number. Pressing \ separates the second number to
be entered from the first number already entered.
20 Section 1: Getting Started
In summary, to perform an arithmetic operation:
1. Key in the first number.
2. Press \ to separate the second number from the first.
3. Key in the second number.
4. Press +,-,§, or z to perform the desired operation.
For example to calculate 13 ÷ 2, proceed as follows:
Keystrokes (RPN mode)Display
13
\
2
z
Notice that after you pressed \, two zeroes appeared following the decimal
point. This is nothing magical: the calculator’s display is currently set to show
two decimal places of every number that has been entered or calculated. Before
you pressed \, the calculator had no way of knowing that you had completed
entering the number, and so displayed only the digits you had keyed in. Pressing
\ tells the calculator that you have completed entering the number: it
terminates digit entry. You need not press \ after keying in the second
number because the +,-,§, and z keys also terminate digit entry. (In fact,
all keys terminate digit entry except for digit entry keys – digit keys, ., Þ,
and Æ – and prefix keys – f, g, ?, :, and (.)
13.
13.00
2.
6.50
Keys the first number into the
calculator.
Pressing \ separates the second
number from the first.
Keys the second number into the
calculator.
Pressing the operation key
calculates the answer.
Chain Calculations in RPN Mode
Whenever the answer has just been calculated and is therefore in the display, you
can perform another operator with this number by simply keying in the second
number and then pressing the operation key: you need not press \ to separate
the second number from the first. This is because when a number is keyed in
after a function key (such as +,-,§,z, etc.) is pressed, the result of that
prior calculation is stored inside the calculator – just as when the \ key is
pressed. The only time you must press the \ key to separate two numbers is when you are keying them both in, one immediately following the other.
The HP 12C Platinum is designed so that each time you press a function key in
RPN mode, the calculator performs the operation then – not later – so that you
see the results of all intermediate calculations, as well as the “bottom line.”
Section 1: Getting Started21
Example: Suppose you’ve written three checks without updating your
checkbook, and you’ve just deposited your paycheck for $1,053.00 into your
checking account. If your latest balance was $58.33 and the checks were written
for $22.95, $13.70, and $10.14, what is the new balance?
Solution: When written down on paper, this problem would read
58.33 – 22.95 – 13.70 – 10.14 + 1053
Keystrokes (RPN mode)Display
58.33
\
22.95
-
13.70
-
10.14-
1053+
58.33
58.33
22.95
35.38
13.70
21.68
11.54
1,064.54
Keys the first number.
Pressing \ separates the second
number from the first.
Keys in the second number.
Pressing - subtracts the second
number from the first. The
calculator displays the result of this
calculation, which is the balance
after subtracting the first check.
Keys in the next number. Since a
calculation has just been
performed, do not press \; the
next number entered (13.70) is
automatically separated from the
one previously in the display
(35.38).
Pressing - subtracts the number
just entered from the number
previously in the display. The
calculator displays the result of this
calculation, which is the balance
after subtracting the second check.
Keys in the next number and
subtracts it from the previous
balance. The new balance appears
in the display. (It’s getting rather
low!)
Keys in the next number – the
paycheck deposited – and adds it to
the previous balance. The new,
current balance appears in the
display.
22 Section 1: Getting Started
The preceding example demonstrates how the HP 12C Platinum calculates just
as you would using pencil and paper (except a lot faster!):
Youdooneoperationatatime...
...andyouseetheresultsofeachoperationimmediately.
Let’s see this happening in a different type of calculation – one that involves
multiplying groups of two numbers and then adding the results. (This is the type
of calculation that would be required to total up an invoice consisting of several
items with different quantities and different prices.)
For example, consider the calculation of (3 × 4) + (5 × 6). If you were doing this
on paper, you would first do the multiplication in the first parentheses, then the
multiplication in the second parentheses, and finally add the results of the two
multiplications:
Your HP 12C Platinum calculates the answer in just the same way:
Keystrokes (RPN mode)Display
3\4§
5\6§
+
12.00
30.00
42.00
Step 1: Multiply the numbers in the
first parentheses.
Step 2: Multiply the numbers in the
second parentheses.
Step 3: Add the results of the two
multiplications.
Notice that before doing step 2, you did not need to store or write down the result
of step 1: it was stored inside the calculator automatically. And after you keyed
in the 5 and the 6 in step 2, the calculator was holding two numbers (12 and 5)
inside for you, in addition to the 6 in the display. (The HP 12C Platinum can hold
a total of three numbers inside, in addition to the number in the display.) After
step 2, the calculator was still holding the 12 inside for you, in addition to the 30
in the display. You can see that the calculator holds the number for you, just as
you would have them written on paper, and then calculates with them at the
Section 1: Getting Started23
proper time, just as you would yourself.2 But with the HP 12C Platinum, you
don’t need to write down the results of an intermediate calculation, and you don’t
even need to manually store it and recall it later.
By the way, notice that in step 2 you needed to press \ again. This is simply
because you were again keying in two numbers immediately following each
other, without performing a calculation in between.
To check your understanding of how to calculate with your HP 12C Platinum, try
the following problems yourself. Although these problems are relatively simple,
more complicated problems can be solved using the same basic steps. If you
have difficulty obtaining the answers shown, review the last few pages.
34+()56+()×77.00=
27 14–()
-----------------------0.25=
14 38+()
5
---------------------------0 . 1 3=
31621++
Storage Registers
Numbers (data) in the HP 12C Platinum are stored in memories called “storage
registers” or simply “registers.” (The singular term “memory” is sometimes used
in this handbook to refer to the entire collection of storage registers.) Four
special registers are used for storing numbers during calculations (these “stack
registers” are described in Appendix A), and another (called the “LAST X”
register) is used for storing the number last in the display before an operation is
performed. In addition to these registers into which numbers are stored
automatically, up to 20 “data storage” registers are available for manual storage
of numbers. These data storage registers are designated R
through R.9. Fewer registers are available for data storage if a program has been
stored in the calculator (since the program is stored in some of those 20
registers), but a minimum of 7 registers is always available. Still other storage
registers – referred to as the “financial registers” – are reserved for numbers used
in financial calculations.
through R9 and R
0
.0
2.
Although you don’t need to know just how these numbers are stored and brought back at just
the right time, if you’re interested you can read all about it in Appendix A. By gaining a more
complete understanding of the calculator’s operation, you’ll use it more efficiently and
confidently, yielding a better return on the investment in your HP 12C Platinum.
24 Section 1: Getting Started
Storing and Recalling Numbers
To store the number from the display into a data storage register:
1. Press ? (store).
2. Key in the register number: 0 through 9 for registers R
through .9 for registers R
through R.9.
.0
Similarly, to recall a number from a storage register into the display, press :
(recall), then key in the register number. This copies the number from the storage
register into the display; the number remains unaltered in the storage register.
Furthermore, when this is done, the number previously in the display is
automatically held inside the calculator for a subsequent calculation, just as the
number in the display is held when you key in another number.
Example: Before you leave to call on a customer interested in your personal
computer, you store the cost of the computer ($3,250) and also the cost of a
printer ($2,500) in data storage registers. Later, the customer decides to buy six
computers and one printer. You recall the cost of the computer, multiply by the
quantity ordered, and then recall and add the cost of the printer to get the total
invoice.
Keystrokes (RPN mode)Display
3250?1
2500?2
3,250.00
2,500.00
;Turns the calculator off.
Stores the cost of the computer in
R
.
1
Stores the cost of the printer in R2.
through R9, or .0
0
Later that same day …
Keystrokes (RPN mode)Display
;
:1
6§
:2
+
2,500.00
3,250.00
19,500.00
2,500.00
22,000.00
Turns the calculator back on.
Recalls the cost of the computer to
the display.
Multiplies the quantity ordered to
get the cost of the computers.
Recalls the cost of the printer to the
display.
Total invoice.
Section 1: Getting Started25
Clearing Storage Registers
To clear a single storage register – that is, to replace the number in it with zero –
merely store zero into it. You need not clear a storage register before storing data
into it; the storing operation automatically clears the register before the data is
stored.
To clear all storage registers at once – including the financial registers, the stack
registers, and the LAST X register – press fCLEARH.
3
This also clears the
display.
All storage registers are also cleared when Continuous Memory is reset (as
described on page 70).
Storage Register Arithmetic
Suppose you wanted to perform an arithmetic operation with the number in the
display and the number in a storage register, then store the result back into the
same register without altering the number in the display. The HP 12C Platinum
enables you to do all this in a single operation.
1. Press ?.
2. Press +,-,§, or z to specify the desired operation.
3. Key in the register number.
When storage register arithmetic is performed, the new number in the register is
determined according to the following rule:
numberformerly
inregister
Storage register arithmetic is possible with only registers R
numberindisplay
through R
0
4
.
Example: In the example on page 21, we updated the balance in your
checkbook. Let’s suppose that because data is stored indefinitely in your
calculator’s Continuous Memory, you keep track of your checking account
balance in the calculator. You could use storage register arithmetic to quickly
update the balance after depositing or writing checks.
3.
CLEARH is not programmable.
26 Section 1: Getting Started
KeystrokesDisplay
58.33?0
22.95?-0
13.70?-0
10.14?-0
1053?+0
:0
58.33
22.95
13.70
10.14
1,053.00
1,064.54
Stores the current balance in
register R
.
0
Subtracts the first check from the
balance in R
. Note that the display
0
continues to show the amount
subtracted; the answer is placed
only in R
.
0
Subtracts the second check.
Subtracts the third check.
Adds the deposit.
Recalls the number in R0 to check
the new balance.
Section 2
Percentage and Calendar
Functions
Percentage Functions
The HP 12C Platinum includes three keys for solving percentage problems: b,
à, and Z. You don’t need to convert percentages to their decimal
equivalents; this is done automatically when you press any of these keys. Thus,
4% need not be changed to 0.04; you key it in the way you see and say it: 4b.
Percentages
In RPN mode, to find the amount corresponding to a percentage of a number:
1. Key in the base number.
2. Press \.
3. Key in the percentage.
4. Press b.
For example, to find 14% of $300:
Keystrokes (RPN mode)Display
300
\
14
b
300.
300.00
14.
42.00
Keys in the base number.
Pressing \ separates the next
number entered from the first
number, just as when an ordinary
arithmetic calculation is performed.
Keys in the percentage.
Calculates the amount.
If the base number is already in the display as a result of a previous calculation,
you should not press \ before keying in the percentage – just as in a chain
arithmetic calculation.
Net Amount
A net amount – that is, the base amount plus or minus the percentage amount –
can be calculated easily with your HP 12C Platinum, since the calculator holds
27
28 Section 2: Percentage and Calendar Functions
the base amount inside after you calculate a percentage amount. To calculate a
net amount, simply calculate the percentage amount, then press = or -.
Example: You’re buying a new car that lists for $13,250. The dealer offers you a
discount of 8%, and the sales tax is 6%. Find the amount the dealer is charging
you, then find the total cost to you, including tax.
Keystrokes (RPN mode)Display
13250\
8b
6b
=
13,250.00
1,060.00
12,190.00
731.40
12,921.40
Keys in the base amount and
separates it from the percentage.
Amount of discount.
Base amount less discount.
Amount of tax (on $12,190).
Total cost: base amount less
discount plus tax.
Percent Difference
In RPN mode, to find the percent difference between two numbers:
1. Key in the base number.
2. Press \ to separate the other number from the base number.
3. Key in the other number.
4. Press à.
If the other number is greater than the base number, the percent difference will
be positive. If the other number is less than the base number, the percent
difference will be negative. Therefore, a positive answer indicates an increase,
while a negative answer indicates a decrease.
If you are calculating a percent difference over time, the base number is typically
the amount occurring first.
Example: Yesterday your stock fell from 58˝ to 53ď per share. What is the
percent change?
KeystrokesDisplay
58.5\
53.25
à
The à key can be used for calculations of the percent difference between a
wholesale cost and a retail cost. If the base number entered is the wholesale cost,
58.50
53.25
–8.97
Keys in the base number and
separates it from the other number.
Keys in the other number.
Nearly a 9% decrease.
Section 2: Percentage and Calendar Functions29
the percent difference is called the markup; if the base number entered is the
retail cost, the percent difference is called the margin. Examples of markup and
margin calculations are included in the HP 12C Platinum Solutions Handbook.
Percent of Total
In RPN mode, to calculate what percentage one number is of another:
1. Calculate the total amount by adding the individual amounts, just as in a
chain arithmetic calculation.
2. Key in the number whose percentage equivalent you wish to find.
3. Press Z.
Example: Last month, your company posted sales of $3.92 million in the U.S.,
$2.36 million in Europe, and $1.67 million in the rest of the world. What
percentage of the total sales occurred in Europe?
Keystrokes (RPN mode)Display
3.92\
2.36+
1.67+
2.36
Z
3.92
6.28
7.95
2.36
29.69
Keys in the first number and
separates it from the second.
Adds the second number.
Adds the third number to get the
total.
Keys in 2.36 to find what
percentage it is of the number in the
display.
Europe had nearly 30% of the total
sales.
The HP 12C Platinum holds the total amount inside after a percent of total is
calculated. Therefore, to calculate what percentage another amount is of the
total:
1. Clear the display by pressing O.
2. Key in that amount.
3. Press Z again.
For example, to calculate what percent of the total sales in the preceding
example occurred in the U.S. and what percent occurred in the rest of the world:
Keystrokes (RPN mode)Display
O3.92Z
O1.67 Z
49.31
21.01
The U.S. had about 49% of the total
sales.
The rest of the world had about
21% of the total sales.
30 Section 2: Percentage and Calendar Functions
To find what percentage a number is of a total, when you already know the total
number
1. Key in the total number.
2. Press \ to separate the other number from the total number.
3. Key in the number whose percentage equivalent you wish to find.
4. Press Z.
For example, if you already knew in the preceding example that the total sales
were $7.95 million and you wanted to find what percentage of that total occurred
in Europe:
KeystrokesDisplay
7.95\
2.36
Z
7.95
2.36
29.69
Keys in the total amount and
separates it from the next number.
Keys in 2.36 to find what
percentage it is of the number in the
display.
Europe had nearly 30% of the total
sales.
Calendar Functions
The calendar functions provided by the HP 12C Platinum – D and Ò – can
handle dates from October 15, 1582 through November 25, 4046.
Date Format
For each of the calendar functions – and also for bond calculations (E and
S) – the calculator uses one of two date formats. The date format is used to
interpret dates when they are keyed into the calculator as well as for displaying
dates.
Month-Day-Year. To set the date format to month-day-year, press gÕ. To
key in a date with this format in effect:
1. Key in the one or two digits of the month.
2. Press the decimal point key (.).
3. Key in the two digits of the day.
4. Key in the four digits of the year.
Dates are displayed in the same format.
Section 2: Percentage and Calendar Functions31
For example, to key in April 7, 2004:
KeystrokesDisplay
4.072004
Day-Month-Year. To set the date format to day-month-year, press gÔ. To
key in a date with this format in effect:
1. Key in the one or two digits of the day.
2. Press the decimal point key (.).
3. Key in the two digits of the month.
4. Key in the four digits of the year.
For example, to key in 7 April, 2004:
4.072004
KeystrokesDisplay
7.042004
When the date format is set to day-month-year, the D.MY status indicator in the
display is lit. If D.MY is not lit, the date format is set to month-day-year.
The date format remains set to what you last specified until you change it; it is
not reset each time the calculator is turned on. However, if Continuous Memory
is reset, the date format is set to month-day-year.
7.042004
Future or Past Dates
To determine the date and day that is a given number of days from a given date:
1. Key in the given date and press \.
2. Key in the number of days.
3. If the other date is in the past, press Þ.
4. Press gD.
The answer calculated by the D function is displayed in a special format. The
numbers of the month, day, and year (or day, month, and year) are separated by
digit separators, and the digit at the right of the displayed answer indicates the
day of the week: 1 for Monday through 7 for Sunday.
4.
The day of the week indicated by the D function may differ from that recorded in history
for dates when the Julian calendar was in use. The Julian calendar was standard in England
and its colonies until September 14, 1752, when they switched to the Gregorian calendar.
Other countries adopted the Gregorian calendar at various times.
4
32 Section 2: Percentage and Calendar Functions
Example: If you purchased a 120-day option on a piece of land on 14 May 2004,
what would be the expiration date? Assume that you normally express dates in
the day-month-year format.
KeystrokesDisplay
gÔ
14.052004\
120gD
When D is executed as an instruction in a running program, the calculator
pauses for about 1 second to display the result, then resumes program execution.
7.04
14.05
11,09,2004 6
Sets date format to day-monthyear. (Display shown assumes
date remains from preceding
example. The full date is not
now displayed because the
display format is set to show
only two decimal places, as
described in Section 5.)
Keys in date and separates it
from number of days to be
entered.
The expiration date is 11
September 2004, a Saturday.
Number of Days Between Dates
To calculate the number of days between two given dates:
1. Key in the earlier date and press \.
2. Key in the later date and press gÒ.
The answer shown in the display is the actual number of days between the two
dates, including leap days (the extra days occurring in leap years), if any. In
addition, the HP 12C Platinum also calculates the number of days between the
two dates on the basis of a 30-day month. This answer is held inside the
calculator; to display it, press ~. Pressing ~ again will return the original
answer to the display.
Example: Simple interest calculations can be done using either the actual
number of days or the number of days counted on the basis of a 30-day month.
What would be the number of days counted each way, to be used in calculating
the simple interest accruing from June 3, 2004 to October 14, 2005? Assume that
you normally express dates in the month-day-year format.
Section 2: Percentage and Calendar Functions33
KeystrokesDisplay
gÕ
6.032004\
10.152005gÒ
~
11.09
6.03
498.00
491.00
Sets date format to month-day-year.
(Display shown assumes date
remains from preceding example.)
Keys in earlier date and separates it
from the later date.
Keys in later date. Display shows
actual number of days.
Number of days counted on the
basis of a 30-day month.
Section 3
Basic Financial Functions
The Financial Registers
In addition to the data storage registers discussed on page 23, the HP 12C
Platinum has five special registers in which numbers are stored for financial
calculations. These registers are designated n, i, PV, PMT, and FV. The first five
keys on the top row of the calculator are used to store a number from the display
into the corresponding register, to calculate the corresponding financial value
and store the result into the corresponding register, or to display the number
stored in the corresponding register.
Storing Numbers Into the Financial Registers
To store a number into a financial register, key the number into the display, then
press the corresponding key (n, ¼, $, P, or M).
Displaying Numbers in the Financial Registers
5
To display a number stored in a financial register, press : followed by the
corresponding key.
6
Clearing the Financial Registers
Every financial function uses numbers stored in several of the financial registers.
Before beginning a new financial calculation, it is good practice to clear all of
the financial registers by pressing fCLEARG. Frequently, however, you
may want to repeat a calculation after changing a number in only one of the
financial registers. To do so, do not press fCLEARG; instead, simply store
the new number in the register. The numbers in the other financial registers
remain unchanged.
5.
Which operation is performed when one of these keys is pressed depends upon the last
preceding operation performed: If a number was just stored into a financial register (using
n, ¼, $, P, M, A, or C), pressing one of these five keys calculates the
corresponding value and stores it into the corresponding register; otherwise pressing one of
these five keys merely stores the number from the display into the corresponding register.
6.
It’s good practice to press the corresponding key twice after :, since often you may want
to calculate a financial value right after displaying another financial value. As indicated in the
preceding footnote, if you wanted to display FV and then calculate PV, for example, you
should press :MM$. If you didn’t press M the second time, pressing
store FV in the PV register rather than calculating PV, and to calculate PV you would have to
press $ again.
34
$ would
Section 3: Basic Financial Functions35
The financial registers are also cleared when you press fCLEARH and
when Continuous Memory is reset (as described on page 70).
Simple Interest Calculations
The HP 12C Platinum simultaneously calculates simple interest on both a 360day basis and a 365-day basis. You can display either one, as described below.
Furthermore, with the accrued interest in the display, you can calculate the total
amount (principal plus accrued interest) by pressing +.
1. Key in or calculate the number of days, then press n.
2. Key in the annual interest rate, then press ¼.
3. Key in the principal amount, then press Þ$.
4. Press fÏ to calculate and display the interest accrued on a 360-day
basis.
5. If you want to display the interest accrued on a 365-day basis, press
d~.
6. Press + to calculate the total of the principal and the accrued interest now
in the display.
The quantities n, i, and PV can be entered in any order.
Example 1: Your good friend needs a loan to start his latest enterprise and has
requested that you lend him $450 for 60 days. You lend him the money at 7%
simple interest, to be calculated on a 360-day basis. What is the amount of
accrued interest he will owe you in 60 days, and what is the total amount owed?
7
Keystrokes (RPN mode)Display
60n
7¼
450Þ$
fÏ
+
60.00
7.00
–450.00
5.25
455.25
Example 2: Your friend agrees to the 7% interest on the loan from the preceding
example, but asks that you compute it on a 365-day basis rather than a 360-day
7.
Pressing the $ key stores the principal amount in the PV register, which then contains the
present value of the amount on which interest will accrue. The Þ key is pressed first to
change the sign of the principal amount before storing it in the PV register. This is required
by the cash flow sign convention, which is applicable primarily to compound interest
calculations.
Stores the number of days.
Stores the annual interest rate.
Stores the principal.
Accrued interest, 360-day basis.
Total amount: principal plus
accrued interest.
36 Section 3: Basic Financial Functions
basis. What is the amount of accrued interest he will owe you in 60 days, and
what is the total amount owed?
Keystrokes (RPN mode)Display
60n
7¼
450Þ$
fÏd~
+
60.00
7.00
–450.00
5.18
455.18
If you have not altered the
numbers in the n, i, and PV
registers since the preceding
example, you may skip these
keystrokes.
Accrued interest, 365-day
basis.
Total amount: principal plus
accrued interest.
Financial Calculations and the Cash Flow Diagram
The concepts and examples presented in this section are representative of a wide
range of financial calculations. If your specific problem does not appear to be
illustrated in the pages that follow, don’t assume that the calculator is not capable
of solving it. Every financial calculation involves certain basic elements; but the
terminology used to refer to these elements typically differs among the various
segments of the business and financial communities. All you need to do is
identify the basic elements in your problem, and then structure the problem so
that it will be readily apparent what quantities you need to tell the calculator and
what quantity you want to solve for.
An invaluable aid for using your calculator in a financial calculation is the cashflow diagram. This is simply a pictorial representation of the timing and
direction of financial transactions, labeled in terms that correspond to keys on
the calculator.
The diagram begins with a horizontal line, called a time line. It represents the
duration of a financial problem, and is divided into compounding periods. For
example, a financial problem that transpires over 6 months with monthly
compounding would be diagrammed like this:
The exchange of money in a problem is depicted by vertical arrows. Money you
receive is represented by an arrow pointing up from the point in time line when
the transaction occurs; money you pay out is represented by an arrow pointing
down.
Section 3: Basic Financial Functions37
Moneypaidout
Moneyreceived
Suppose you deposited (paid out) $1,000 into an account that pays 6% annual
interest and is compounded monthly, and you subsequently deposited an
additional $50 at the end of each month for the next 2 years. The cash flow
diagram describing the problem would look like this:
The arrow pointing up at the right of the diagram indicates that money is
received at the end of the transaction. Every completed cash flow diagram must
include at least one cash flow in each direction. Note that cash flows
corresponding to the accrual of interest are not represented by arrows in the cash
flow diagram.
The quantities in the problem that correspond to the first five keys on the top row
of the keyboard are now readily apparent from the cash flow diagram.
z n is the number of compounding periods. This quantity can be expressed in
years, months, days, or any other time unit, as long as the interest rate is
expressed in terms of the same basic compounding period. In the problem
illustrated in the cash flow diagram above, n = 2 × 12.
The form in which n is entered determines whether or not the calculator
performs financial calculations in Odd-Period mode (as described on pages
51 through 54). If n is a noninteger (that is, there is at least one nonzero
digit to the right of the decimal point), calculations of i, PV, PMT, and FV
are performed in Odd-Period mode.
38 Section 3: Basic Financial Functions
z i is the interest rate per compounding period. The interest rate shown in the
cash flow diagram and entered into the calculator is determined by
dividing the annual interest rate by the number of compounding periods. In
the problem illustrated above, i = 6% ÷ 12.
z PV – the present value – is the initial cash flow or the present value of a
series of future cash flows. In the problem illustrated above, PV is the
$1,000 initial deposit.
z PMT is the period payment. In the problem illustrated above PMT is the
$50 deposited each month. When all payments are equal, they are referred
to as annuities. (Problems involving equal payments are described in this
section under Compound Interest Calculations; problems involving
unequal payments can be handled as described in Section 4 under
Discounted Cash Flow Analysis: NPV and IRR. Procedures for calculating
the balance in a savings account after a series of irregular and/or unequal
deposits are included in the HP 12C Platinum Solutions Handbook.)
z FV – the future value – is the final cash flow or the compounded value of a
series of prior cash flows. In the particular problem illustrated above, FV is
unknown (but can be calculated).
Solving the problem is now basically a matter of keying in the quantities
identified in the cash flow diagram using the corresponding keys, and then
calculating the unknown quantity by pressing the corresponding key. In the
particular problem illustrated in the cash flow diagram above, FV is the unknown
quantity; but in other problems, as we shall see later, n, i, PV, or PMT could be
the unknown quantity. Likewise, in the particular problem illustrated above there
are four known quantities that must be entered into the calculator before solving
for the unknown quantity; but in other problems only three quantities may be
known – which must always include n or i.
The Cash Flow Sign Convention
When entering the PV, PMT, and FV cash flows, the quantities must be keyed
into the calculator with the proper sign, + (plus) or – (minus), in accordance with
…
The Cash Flow Sign Convention: Money received (arrow pointing up) is
entered or displayed as a positive value (+). Money paid out (arrow
pointing down) is entered or displayed as a negative value (–).
The Payment Mode
One more bit of information must be specified before you can solve a problem
involving periodic payments. Such payments can be made either at the beginning
of a compounding period (payments in advance, or annuities due) or at the end of
the period (payments in arrears, or ordinary annuities). Calculations involving
Section 3: Basic Financial Functions39
payments in advance yield different results than calculations involving payments
in arrears. Illustrated below are portions of cash flow diagrams showing
payments in advance (Begin) and payments in arrears (End). In the problem
illustrated in the cash flow diagram above, payments are made in arrears.
Begin
Regardless of whether payments are made in advance or in arrears, the number
of payments must be the same as the number of compounding periods.
To specify the payment mode:
z Press g× if payments are made at the beginning of the compounding
periods.
z Press g if payments are made at the end of the compounding
periods.
The BEGIN status indicator is lit when the payment mode is set to Begin. If
BEGIN is not lit, the payment mode is set to End.
The payment mode remains set to what you last specified until you change it; it
is not reset each time the calculator is turned on. However, if Continuous
Memory is reset, the payment mode will be set to End.
End
Generalized Cash Flow Diagrams
Examples of various kinds of financial calculations, together with the applicable
cash flow diagrams, appear under Compound Interest Calculations later in this
section. If your particular problem does not match any of those shown, you can
solve it nevertheless by first drawing a cash flow diagram, then keying the
quantities identified in the diagram into the corresponding registers. Remember always to observe the sign convention when keying in PV, PMT, and FV.
The terminology used for describing financial problems varies among the
different segments of the business and financial communities. Nevertheless,
most problems involving compound interest can be solved by drawing a cash
flow diagram in one of the following basic forms. Listed below each form are
some of the problems to which that diagram applies.
40 Section 3: Basic Financial Functions
CompoundGrowth
SavingsAccount
Appreciation
Mortgage
DirectReduction(Installment)Loan
Amortization
OrdinaryAnnuity
Amortization
AnnuityDue
SavingsPlan
PensionFund
AnnuityDue
MortgageWithBalloon
Amortization
OrdinaryAnnuity
Lease
LeaseWithBuyback(Residual)
Amortization
AnnuityDue
Section 3: Basic Financial Functions41
Compound Interest Calculations
Specifying the Number of Compounding Periods and the
Periodic Interest Rate
Interest rates are usually quoted at the annual rate (also called the nominal rate):
that is, the interest rate per year. However, in compound interest problems, the
interest rate entered into i must always be expressed in terms of the basic
compounding period, which may be years, months, days, or any other time unit.
For example, if a problem involves 6% annual interest compounded quarterly for
5 years, n – the number of quarters – would be 5 × 4 = 20 and i – the interest rate
per quarter – would be 6% ÷ 4 = 1.5%. If the interest were instead compounded
monthly, n would be 5× 12 = 60 and i would be 6% ÷ 12 = 0.5%.
If you use the calculator to multiply the number of years by the number of
compounding periods per year, pressing n then stores the result in n. The same
is true for i. Values of n and i are calculated and stored like this in Example 2 on
page 48.
If interest is compounded monthly, you can use a shortcut provided on the
calculator to calculate and store n and i:
z To calculate and store n, key the number of years into the display, then
press gA.
z To calculate and store i, key the annual rate into the display, then press
gC.
Note that these keys not only multiply or divide the displayed number by 12;
they also automatically store the result in the corresponding register, so you need
not press the n or ¼ key next. The A and C keys are used in Example 1
on page 48.
Calculating the Number of Payments or Compounding
Periods
1. Press fCLEARG to clear the financial registers.
2. Enter the periodic interest rate, using ¼ or C.
3. Enter at least two of the following values:
z Present value, using $.
z Payment amount, using P.
z Future value, using M.
4. If a PMT was entered, press g× or g to set the payment mode.
5. Press n to calculate the number of payments or periods.
Note: Remember to
observe the cash flow
sign convention.
42 Section 3: Basic Financial Functions
If the answer calculated is not an integer (that is, there would be nonzero digits to
the right of the decimal point), the calculator rounds the answer up to the next
8
higher integer before storing it in the n register and displaying it.
For example,
if n were calculated as 318.15, 319.00 would be the displayed answer.
n is rounded up by the calculator to show the total number of payments needed:
n–1 equal, full payments, and one final, smaller payment. The calculator does
not automatically adjust the values in the other financial registers to reflect
n equal payments; rather, it allows you to choose which, if any, of the values to
9
adjust.
Therefore, if you want to know the value of the final payment (with
which you can calculate a balloon payment) or desire to know the payment value
for n equal payments, you will need to press one of the other financial keys, as
shown in the following two examples.
Example 1: You’re planning to build a log cabin on your vacation property. Your
rich uncle offers you a $35,000 loan at 10.5% interest. If you make $325
payments at the end of each month, how many payments will be required to pay
off the loan, and how many years will this take?
Keystrokes(RPN mode)Display
fCLEARG
10.5gC
35000$
325ÞP
gÂ
n
12z
8.
The calculator will round n down to the next lower integer if the fractional portion of n is less
than 0.005.
9.
After calculating n, pressing ¼,$,P, or M will recalculate the value in the
corresponding financial register.
0.88
35,000.00
–325.00
–325.00
328.00
27.33
Calculates and stores i.
Stores PV.
Stores PMT (with minus sign for
cash paid out).
Sets the payment mode to End.
Number of payments required.
Twenty-seven years and four
months.
Section 3: Basic Financial Functions43
Because the calculator rounds the calculated value of n up to the next higher
integer, in the preceding example it is likely that – while 328 payments will be
required to pay off the loan – only 327 full payments of $325 will be required,
the next and final payment being less than $325. You can calculate the final,
fractional, 328th payment as follows:
Keystrokes (RPN mode)Display
328n
M
328.00
181.89
Stores total number of payments.
Calculates FV – which equals the
overpayment if 328 full payments
were made.
:P
+
aYou could skip this step, since 328 is already stored in the n register. If you do so, how-
ever, you will need to press M twice in the next step (for the reason discussed in the
first footnote on page 34; you would not have to press M twice if you had not pressed
12z after w in the example above.) We choose to show this and the following example in a parallel format so that the procedure is easy to remember: the number you key
is the number of the final payment—either the fractional payment or the balloon payment—whose amount is to be calculated.
Alternatively, you could make the fractional payment together with the 327th
payment. (Doing so will result in a somewhat smaller total of all payments, since
you will not have to pay interest during the 328th payment period.) You can
calculate this final, larger, 327th payment (essentially a balloon payment) as
follows:
a
Keystrokes (RPN mode)Display
327n
M
:P
+
327.00
–141.87
–325.00
–466.87
Instead of having a fractional (or balloon) payment at the end of the loan, you
might wish to make 327 or 328 equal payments. Refer to “Calculating the
Payment Amount” on page 48 for a complete description of this procedure.
Example 2: You’re opening a savings account today (the middle of the month)
with a $775 deposit. The account pays 6ď% interest compounded semimonthly.
If you make semimonthly deposits of $50 beginning next month, how long will it
take for your account to reach $4000?
Stores number of full payments.
Calculates FV – which is the
balance remaining after 327 full
payments.
Recalls payment amount.
Final, balloon payment.
44 Section 3: Basic Financial Functions
Keystrokes (RPN mode)Display
fCLEARG
6.25\24z¼
775Þ$
50ÞP
4000M
gÂ
n
2z
0.26
–775.00
–50.00
4,000.00
4,000.00
58.00
29.00
Calculates and stores i.
Stores PV (with minus sign for cash
paid out).
Stores PMT (with minus sign for
cash paid out).
Stores FV.
Sets the payment mode to End.
Number of semimonthly deposits.
Number of months.
As in Example 1, it is likely that only 57 full deposits will be required, the next
and final deposit being less than $50. You can calculate this final, fractional, 58th
deposit as in Example 1, except that for this example you must subtract the
original FV. (In Example 1, the original FV was zero.) The procedure is as
follows:
Keystrokes (RPN mode)Display
MM
:P
+
4000-
4,027.27
–50.00
3,977.27
–22.73
Calculates FV – which equals the
balance in the account if 58 full
deposits were made.
a
Recalls amount of deposits.
Calculates the balance in the
account if 57 full deposits were
made and interest accrued during
th
the 58
Calculates final, fractional, 58
month.
b
th
deposit required to reach $4,000.
Section 3: Basic Financial Functions45
aIn this example, M must be pressed twice, since the preceding key pressed was z.
If we had stored the number of deposits in n (as we did following Example 1), we
would have to press M only once here, since the preceding key pressed would have
been w (as it was following Example 1). Remember that it is not necessary to store
the number of payments in n before calculating the amount of the final, fractional payment. (Refer to the preceding footnote.)
bYou might think that we could calculate the balance in the account after 57 full deposits
were made simply by storing that number in n and then calculating FV, as we did using
the second method following Example 1. However, this balance would not include the
interest accrued during the 58
th
month.
Calculating the Periodic and Annual Interest Rates
1. Press fCLEARG to clear the financial registers.
2. Enter the number of payments or periods, using n or A.
3. Enter at least two of the following values:
z Present value, using $.
z Payment amount, using P.
z Future value, using M.
4. If a PMT was entered, press g× or g to set the payment mode.
5. Press ¼ to calculate the periodic interest rate.
6. To calculate the annual interest rate, key in the number of periods per year,
then press §.
Note: Remember to
observe the cash flow
sign convention.
Example: What annual interest rate must be obtained to accumulate $10,000 in
8 years on an investment of $6,000 with quarterly compounding?
1. Press fCLEARG to clear the financial registers.
2. Enter the number of payments or periods, using n or A.
3. Enter the periodic interest rate, using ¼ or C.
4. Enter either or both of the following:
z Payment amount, using P.
z Future value, using M.
5. If a PMT was entered, press g× or g to set the payment mode.
6. Press $ to calculate the present value.
Note: Remember to
observe the cash flow
sign convention.
Example 1: You’re financing a new car purchase with a loan from an institution
that requires 15% interest compounded monthly over the 4-year term of the loan.
If you can make payments of $150 at the end of each month and your down
payment will be $1,500, what is the maximum price you can pay for the car?
(Assume the purchase date is one month prior to the date of the first payment.)
Section 3: Basic Financial Functions47
Keystrokes(RPN mode)Display
fCLEARG
4gA
15gC
150ÞP
gÂ
$
1500+
Example 2: A development company would like to purchase a group of
condominiums with an annual net cash flow of $17,500. The expected holding
period is 5 years, and the estimated selling price at that time is $540,000.
Calculate the maximum amount the company can pay for the condominiums in
order to realize at least a 12% annual yield.
48.00
1.25
–150.00
–150.00
5,389.72
6,889.72
Calculates and stores n.
Calculates and stores i.
Stores PMT (with minus sign for
cash paid out).
Sets payment mode to End.
Maximum amount of loan.
Maximum purchase price.
KeystrokesDisplay
fCLEARG
5n
12¼
17500P
540000M
gÂ
$
5.00
12.00
17,500.00
540,000.00
540,000.00
–369,494.09
Stores n.
Stores i.
Stores PMT. Unlike in the
previous problem, here PMT
is positive since it represents
cash received.
Stores FV.
Sets payment mode to End.
The maximum purchase price
to provide a 12% annual
yield. PV is displayed with a
minus sign since it represents
cash paid out.
48 Section 3: Basic Financial Functions
Calculating the Payment Amount
1. Press fCLEARG to clear the financial registers.
2. Enter the number of payments or periods, using n or A.
3. Enter the periodic interest rate, using ¼ or C.
4. Enter either or both of the following:
z Present value, using $.
z Future value, using M.
5. Press g× or g to set the payment mode.
6. Press P to calculate the payment amount.
Example 1: Calculate the payment amount on a 29-year, $43,400 mortgage at
14ď% annual interest.
Note: Remember to
observe the cash flow
sign convention.
KeystrokesDisplay
fCLEARG
29gA
14.25gC
43400$
gÂ
P
Example 2: Looking forward to retirement, you wish to accumulate $60,000
after 15 years by making deposits in an account that pays 9Đ% interest
compounded semiannually. You open the account with a deposit of $3,200 and
intend to make semiannual deposits, beginning six months later, from your
profit-sharing bonus paychecks. Calculate how much these deposits should be.
348.00
1.19
43,400.00
43,400.00
–523.99
Calculates and stores n.
Calculates and stores i.
Stores PV.
Sets payment mode to End.
Monthly payment (with minus sign
for cash paid out).
Keystrokes(RPN mode)Display
fCLEARG
15\2§n
9.75\2z¼
3200Þ$
60000M
gÂ
P
30.00
4.88
–3200.00
60,000.00
60,000.00
–717.44
Section 3: Basic Financial Functions49
Calculates and stores n.
Calculates and stores i.
Stores PV (with minus sign for cash
paid out).
Stores FV.
Sets payment mode to End.
Semiannual payment (with minus
sign for cash paid out).
Calculating the Future Value
1. Press fCLEARG to clear the financial registers.
2. Enter the number of payments or periods, using n or A.
3. Enter the periodic interest rate, using ¼ or C.
4. Enter either or both of the following:
z Present value, using $.
z Payment amount, using P.
5. If a PMT was entered, press g× or g to set the payment mode.
6. Press M to calculate the future value.
Note: Remember to
observe the cash flow
sign convention.
50 Section 3: Basic Financial Functions
Example 1: In Example 1 on page 48, we calculated that the payment amount on
a 29-year, $43,400 mortgage at 14ď% annual interest is $523.99. If the seller
requests a balloon payment at the end of 5 years, what would be the amount of
the balloon?
KeystrokesDisplay
fCLEARG
5gA
14.25gC
43400$
523.99ÞP
gÂ
M
60.00
1.19
43,400.00
–523.99
–523.99
–42,652.37
Calculates and stores n.
Calculates and stores i.
Stores PV.
Stores PMT (with minus sign for
cash paid out).
Sets payment mode to End.
Amount of balloon payment.
Example 2: If you deposit $50 a month (at the beginning of each month) into a
new account that pays 6ď% annual interest compounded monthly, how much
will you have in the account after 2 years?
Section 3: Basic Financial Functions51
KeystrokesDisplay
fCLEARG
2gA
6.25gC
50ÞP
g×
M
Example 3: Property values in an unattractive area are depreciating at the rate of
2% per year. Assuming this trend continues, calculate the value in 6 years of
property presently appraised at $32,000.
24.00
0.52
–50.00
–50.00
1,281.34
Calculates and stores n.
Calculates and stores i.
Stores PMT (with minus sign for
cash paid out).
Sets payment mode to Begin.
Balance after 2 years.
KeystrokesDisplay
fCLEARG
6n
2Þ¼
32000Þ$
M
6.00
–2.00
–32,000.00
28,346.96
Stores n.
Stores i (with minus sign for a
“negative interest rate”).
Stores PV (with minus sign for cash
paid out).
Property value after 6 years.
Odd-Period Calculations
The cash flow diagrams and examples presented so far have dealt with financial
transactions in which interest begins to accrue at the beginning of the first
regular payment period. However, interest often begins to accrue prior to the
beginning of the first regular payment period. The period from the date interest
begins accruing to the date of the first payment, being not equal to the regular
payment periods is sometimes referred to as an “odd first period”. For simplicity,
in using the HP 12C Platinum we will always regard the first period as equal to
the remaining periods, and we will refer to the period between the date interest
begins accruing and the beginning of the first payment period as simply the “odd
52 Section 3: Basic Financial Functions
period” or the “odd days”. (Note that the odd period is always assumed by the
calculator to occur before the first full payment period.) The following two cash
flow diagrams represent transactions including an odd period for payments in
advance (Begin) and for payments in arrears (End).
.
Begin
odd
period
End
odd
period
You can calculate i, PV, PMT, and FV for transactions involving an odd period
simply by entering a noninteger n. (A noninteger is a number with at least one
nonzero digit to the right of the decimal point.) This places the calculator in OddPeriod mode.
10
The integer part of n (the part to the left of the decimal point)
specifies the number of full payment periods, and the fractional part (the part to
the right of the decimal) specifies the length of the odd period as a fraction of a
full period. The odd period, therefore, cannot be greater than one full period.
The fractional part of n can be determined using either the actual number of odd
days or the number of odd days counted on the basis of a 30-day month.
11
The
Ò function can be used to calculate the number of odd days either way. The
fractional part of n is a fraction of a payment period, so the number of odd days
10.
Calculations of i, PMT, and FV are performed using the present value at the end of the odd
period. This is equal to the number in the PV register plus the interest accrued during the odd
period. When calculating PV in Odd-Period mode, the calculator returns a value equal to the
present value at the beginning of the odd period and stores it in the PV register.
After calculating i, PV, PMT, or FV in Odd-Period mode, you should not try to calculate n. If
you do, the calculator will switch out of Odd-Period mode and compute n without taking the
odd period into account. The values in the other financial registers will correspond to the new
n, but the original assumptions for the problem will be changed.
11.
The two methods of counting odd days will yield slightly different answers. If you are
calculating i to determine the annual percentage rate (APR) for an odd-period transaction, the
lower APR will result if the calculation uses the greater number of odd days determined using
the two methods.
Section 3: Basic Financial Functions53
must be divided by the number of days in a period. If interest is compounded
monthly, for this number you can use either 30, 365/12, or (if the odd period falls
entirely within a single month) the actual number of days in that month. Usually,
a monthly period is taken to be 30 days long.
At your option, the calculations of i, PV, PMT, and FV can be performed with
either simple interest or compound interest accruing during the odd period. If the
C status indicator in the display is not lit, simple interest is used. To specify
12
compound interest, turn the C indicator on by pressing ?Æ.
Pressing
?Æ again turns the C indicator off, and calculations will then be performed
using simple interest for the odd period.
Example 1: A 36-month loan for $4,500 accrues interest at a 15% annual
percentage rate (APR), with the payments made at the end of each month. If
interest begins accruing on this loan on February 15, 2004 (so that the first
period begins on March 1, 2004), calculate the monthly payment, with the odd
days counted on the basis of a 30-day month and compound interest used for the
odd period.
Keystrokes (RPN mode)Display
fCLEARGClears financial registers.
gÕSets date format to month-day-year.
gÂSets payment mode to End.
?ÆTurns on the C indicator in the
display, so that compound interest
will be used for the odd period.
2.152004\
3.012004
gÒ
~
30z
36+n
15gC
4500$
P
2.15
3.012004
15.00
16.00
0.53
36.53
1.25
4,500.00
–157.03
Keys in the date interest begins
accruing and separates it from the
next date entered.
Keys in the date of the beginning of
the first period.
Actual number of odd days.
Number of odd days counted on the
basis of a 30-day month.
Divides by the length of a monthly
period to get the fractional part of n.
Adds the fractional part of n to the
number of complete payment
periods, then stores the result in n.
Calculates and stores i.
Stores PV.
Monthly payment.
12.
?Æ is not programmable.
54 Section 3: Basic Financial Functions
Example 2: A 42-month car loan for $3,950 began accruing interest on July 19,
2004, so that the first period began on August 1, 2004. Payments of $120 are
made at the end of each month. Calculate the annual percentage rate (APR),
using the actual number of odd days and simple interest for the odd period.
Keystrokes (RPN mode)Display
fCLEARGClears financial registers.
?ÆTurns off the C indicator in the
display, so that simple interest will
be used for the odd period.
7.192004\
8.012004
gÒ
30z
42+n
3950$
120ÞP
¼
12§
7.19
8.012004
13.00
0.43
42.43
3,950.00
–120.00
1.16
13.95
Keys in the date interest begins
accruing and separates it from the
next date entered.
Keys in the date of the beginning of
the first period.
Actual number of odd days.
Divides by the length of a monthly
period to get the fractional part of n.
Adds the fractional part of n to the
number of complete payment
periods, then stores the result in n.
The HP 12C Platinum enables you to calculate the amounts applied toward
principal and toward interest from a single loan payment or from several
payments, and also tells you the remaining balance of the loan after the payments
are made.
13.
13
All amounts calculated when f! is pressed are automatically rounded to the number of
decimal places specified by the display format. (The display format is described in Section
5.) This rounding affects the number inside the calculator as well as how the number appears
in the display. The amounts calculated on your HP 12C Platinum may differ from those on
the statements of lending institutions by a few cents, since different rounding techniques are
sometimes used. To calculate answers rounded to a different number of decimal places, press
f followed by the number of decimal places desired before you press f!.
Section 3: Basic Financial Functions55
To obtain an amortization schedule:
1. Press fCLEARG to clear the financial registers.
2. Enter the periodic interest rate, using ¼ or C.
3. Enter the amount of the loan (the principal), using $.
4. Key in the periodic payment, then press ÞP (the sign of PMT must
be negative, in accordance with the cash flow sign convention).
5. Press g× or (for most direct reduction loans) g to set the
payment mode.
6. Key in the number of payments to be amortized.
7. Press f! to display the amount from those payments applied toward
interest.
8. Press ~ to display the amount from those payments applied toward the
principal.
9. To display the number of payments just amortized, press dd.
10. To display the remaining balance of the loan, press :$.
11. To display the total number of payments amortized, press :n.
Example: For a house you’re about to buy, you can obtain a 25-year mortgage
for $50,000 at 13ď% annual interest. This requires payments of $573.35 (at the
end of each month). Find the amounts that would be applied to interest and to the
principal from the first year’s payments.
KeystrokesDisplay
fCLEARG
13.25gC
50000$
573.35ÞP
gÂ
12f!
~
:$
:n
1.10
50,000.00
–573.35
–573.35
–6,608.89
–271.31
49,728.69
12.00
Enters i.
Enters PV.
Enters PMT (with minus sign for
cash paid out).
Sets payment mode to End.
Portion of first year’s payments (12
months) applied to interest.
Portion of first year’s payments
applied to principal.
Balance remaining after 1 year.
Total number of payments
amortized.
56 Section 3: Basic Financial Functions
The number of payments keyed in just before f! is pressed is taken to be
the payments following any that have already been amortized. Thus, if you now
press 12f!, your HP 12C Platinum will calculate the amounts applied to
interest and to the principal from the second year’s payments (that is, the second
12 months):
KeystrokesDisplay
12f!
~
dd
:$
:n
Pressing :$ or :n displays the number in the PV or n register. When
you did so after each of the last two calculations, you may have noticed that PV
and n had been changed from their original values. The calculator does this so
that you can easily check the remaining balance and the total number of
payments amortized. But because of this, if you want to generate a new
amortization schedule from the beginning, you must reset PV to its original value
and reset n to 0.
For example, suppose you now wanted to generate an amortization schedule for
each of the first two months:
–6,570.72
–309.48
12.00
49,419.21
24.00
Portion of second year’s payments
applied to interest.
Portion of second year’s payments
applied to principal.
Number of payments just
amortized.
Balance remaining after 2 years.
Total number of payments
amortized.
Keystrokes Display
50000$
0n
1f!
~
1f!
~
:n
50,000.00
0.00
–552.08
–21.27
–551.85
–21.50
2.00
Resets PV to original value.
Resets n to zero.
Portion of first payment applied to
interest.
Portion of first payment applied to
principal.
Portion of second payment applied
to interest.
Portion of second payment applied
to principal.
Total number of payments
amortized.
Section 3: Basic Financial Functions57
If you want to generate an amortization schedule but do not already know the
monthly payment:
1. Calculate PMT as described on page 48.
2. Press 0n to reset n to zero.
3. Proceed with the amortization procedure listed on page 55 beginning with
step 6.
Example: Suppose you obtained a 30-year mortgage instead of a 25-year
mortgage for the same principal ($50,000) and at the same interest rate (13ď%)
as in the preceding example. Calculate the monthly payment, then calculate the
amounts applied to interest and to the principal from the first month’s payment.
Since the interest rate is not being changed, do not press fCLEARG; to
calculate PMT, just enter the new value for n, reset PV, then press P.
KeystrokesDisplay
30gA
50000$
P
0n
1f!
~
:$
360.00
50,000.00
–562.89
0.00
–552.08
–10.81
49,989.19
Enters n.
Enters PV.
Monthly payment.
Resets n to zero.
Portion of first payment applied to
interest.
Portion of first payment applied to
principal.
Remaining balance.
Section 4
Additional Financial Functions
Discounted Cash Flow Analysis: NPV and IRR
The HP 12C Platinum provides functions for the two most widely-used methods
of discounted cash flow analysis: l (net present value) and L (internal rate of return). These functions enable you to analyze financial problems involving
cash flows (money paid out or received) occurring at regular intervals. As in
compound interest calculations, the interval between cash flows can be any time
period; however, the amounts of these cash flows need not be equal.
To understand how to use l and L, let’s consider the cash flow diagram for
an investment that requires an initial cash outlay (CF
(CF
) at the end of the first year, and so on up to the final cash flow (CF6) at the
1
end of the sixth year. In the following diagram, the initial investment is denoted
, and is depicted as an arrow pointing down from the time line since it is
by CF
0
cash paid out. Cash flows CF
and CF4 also point down from the time line,
1
because they represent projected cash flow losses.
) and generates a cash flow
0
NPV is calculated by adding the initial investment (represented as a negative
cash flow) to the present value of the anticipated future cash flows. The interest
rate, i, will be referred to in this discussion of NPV and IRR as the rate of
14
return.
The value of NPV indicates the result of the investment.
z If NPV is positive, the financial value of the investor’s assets would be
increased: the investment is financially attractive.
z If NPV is zero, the financial value of the investor’s assets would not
change: the investor is indifferent toward the investment.
z If NPV is negative, the financial value of the investor’s assets would be
decreased: the investment is not financially attractive.
14.
Other terms are sometimes used to refer to the rate of return. These include: required rate of return, minimally acceptable rate of return, and cost of capital.
58
Section 4: Additional Financial Functions59
A comparison of the NPV’s of alternative investment possibilities indicates
which of them is most desirable: the greater the NPV, the greater the increase in
the financial value of the investor’s assets.
IRR is the rate of return at which the discounted future cash flows equal the
initial cash outlay: IRR is the discount rate at which NPV is zero. The value of
IRR relative to the present value discount rate also indicates the result of the
investment:
z If IRR is greater than the desired rate of return, the investment is
financially attractive.
z If IRR is equal to the desired rate of return, the investor is indifferent
toward the investment.
z If IRR is less than the desired rate of return, the investment is not
financially attractive.
Calculating Net Present Value (NPV)
Calculating NPV for Ungrouped Cash Flows. If there are no equal
consecutive cash flows, use the procedure described (and then summarized)
below. With this procedure, NPV (and IRR) problems involving up to 30 cash
flows (in addition to the initial investment CF
consecutive cash flows are equal – for example, if the cash flows in periods three
and four are both $8,500 – you can solve problems involving more than 30 cash
flows, or you can minimize the number of storage registers required for
problems involving less than 30 cash flows, by using the procedure described
next (under Calculating NPV for Grouped Cash Flows, page 61).
The amount of the initial investment (CF
the J key.
Note: The initial investment can not be zero.
Each cash flow (CF
, CF2, etc.) is designated CFj, where j takes on values from
1
1 up to the number of the final cash flow. The amount of a cash flow is entered
using the K key. Each time gK is pressed, the amount in the display is
stored in the next available storage register, and the number in the n register is
increased by 1. This register therefore counts how many cash flow amounts (in
addition to the initial investment CF
) have been entered.
0
Note: When entering cash flow amounts – including the initial investment
CF
– remember to observe the cash flow sign convention by pressing
0
Þ after keying in a negative cash flow.
In summary, to enter the cash flow amounts:
1. Press fCLEARH to clear the financial and storage registers.
2. Key in the amount of the initial investment, press Þ if that cash flow is
negative, then press gJ.
) can be solved. If two or more
0
) is entered into the calculator using
0
60 Section 4: Additional Financial Functions
Note: The initial investment can not be zero.
3. Key in the amount of the next cash flow, press Þ if the cash flow is
negative, then press gK. If the cash flow amount is zero in the next
period, press 0 gK.
4. Repeat step 3 for each cash flow until all have been entered.
With the amounts of the cash flows stored in the calculator’s registers, you can
calculate NPV as follows:
1. Enter the interest rate, using ¼ or C.
2. Press fl.
The calculated value of NPV appears in the display and also is automatically
stored in the PV register.
Example: An investor has an opportunity to buy a duplex for $80,000 and would
like a return of at least 13%. He expects to keep the duplex 5 years and then sell
it for $130,000; and he anticipates the cash flows shown in the diagram below.
Calculate NPV to determine whether the investment would result in a return or a
loss.
Note that although a cash flow amount ($4,500) occurs twice, these cash flows
are not consecutive. Therefore, these cash flows must be entered using the
method described above.
KeystrokesDisplay
fCLEARH
80000ÞgJ
500ÞgK
4500gK
5500gK
0.00
–80,000.00
–500.00
4,500.00
5,500.00
Clears financial and storage
registers.
Stores CF0(with minus sign for a
negative cash flow).
Stores CF1(with minus sign for a
negative cash flow).
Stores CF2.
Stores CF3.
Section 4: Additional Financial Functions61
Keystrokes (Cont.)Display
4500gK
130000gK
:n
13¼
fl
4,500.00
130,000.00
5.00
13.00
212.18
Since NPV is positive, the investment would increase the financial value of the
investor’s assets.
Calculating NPV for Grouped Cash Flows. A maximum of 30 cash flow
amounts (in addition to the initial investment CF
Platinum.
15
However, problems involving more than 30 cash flows can be
handled if among the cash flows there are equal consecutive cash flows. For such
problems, you merely enter along with the amounts of the cash flows the number
of times – up to 99 – each amount occurs consecutively. This number is
designated Na key. Each N
, corresponding to cash flow amount CFj, and is entered using the
j
is stored in a special register inside the calculator.
j
This method can, of course, be used for problems involving fewer than 30 cash
flows – and it will require fewer storage registers than the method described
above under Calculating NPV for Ungrouped Cash Flows. Equal consecutive
cash flows can be entered using that method – provided there are enough storage
registers available to accommodate the total number of individual cash flows.
The facility of grouping equal consecutive cash flows is provided to minimize
the number of storage registers required.
Note: When entering cash flow amounts – including the initial investment
CF0 – remember to observe the cash flow sign convention by pressing
Þ after keying in the amount for a negative cash flow.
In summary, to enter the amounts of the cash flows and the number of times they
occur consecutively:
1. Press fCLEARH to clear the financial and storage registers.
2. Key in the amount of the initial investment, press Þ if that cash flow is
negative, then press gJ.
Note: The initial investment can not be zero.
Stores CF4.
Stores CF5.
Checks number of cash flow
amounts entered (in addition to
CF
.
0
Stores i.
NPV.
) can be stored in the HP 12C
0
15.
If you have stored a program in the calculator, the number of registers available for storing
cash flow amounts may be less than 31.
62 Section 4: Additional Financial Functions
3. If the initial investment consists of more than one cash flow of the amount
entered in step 2, key in the number of those cash flows, then press ga.
If ga is not pressed, the calculator assumes that N
is 1.
0
4. Key in the amount of the next cash flow, press Þ if that cash flow is
negative, then press gK. If the cash flow amount is zero in the next
period, press 0gK.
5. If the amount entered in step 4 occurs more than once consecutively, key in
the number of times that cash flow amount occurs consecutively, then
press ga. If ga is not pressed, the calculator assumes that N
for the CF
6. Repeat steps 4 and 5 for each CF
just entered.
j
and Njuntil all cash flows have been
j
is 1
j
entered.
With the amounts of the cash flows and the number of times they occur
consecutively stored in the calculator, NPV can be calculated by entering the
interest rate and pressing fl, just as described earlier.
Example: An investor has an opportunity to purchase a piece of property for
$79,000; and he would like a 13½% return. He expects to be able to sell it after
10 years for $100,000 and anticipates the yearly cash flows shown in the table
below:
YearCash FlowYearCash Flow
1
2
3
4
5
$14,000
$11,000
$10,000
$10,000
$10,000
6
7
8
9
10
$9,100
$9,000
$9,000
$4,500
$100,000
Since two cash flow amounts ($10,000 and $9,000) are repeated consecutively,
we can minimize the number of storage registers required by using the method
just described.
KeystrokesDisplay
fCLEARH
79000ÞgJ
14000gK
11000gK
10000gK
0.00
–79,000.00
14,000.00
11,000.00
10,000.00
Clears financial and storage
registers.
Initial investment (with minus sign
for a negative cash flow).
First cash flow amount
Next cash flow amount.
Next cash flow amount.
Section 4: Additional Financial Functions63
KeystrokesDisplay
3ga
9100gK
9000gK
2ga
4500gK
100000gK
:n
13.5¼
fl
Since NPV is positive, the investment would increase the financial value of the
investor’s assets by $907.77.
3.00
9,100.00
9,000.00
2.00
4,500.00
100,000.00
7.00
13.50
907.77
Number of times this cash flow
amount occurs consecutively.
Next cash flow amount.
Next cash flow amount.
Number of times this cash flow
amount occurs consecutively.
Next cash flow amount.
Final cash flow amount.
Seven different cash flow amounts
have been entered.
Stores i.
NPV
Calculating Internal Rate of Return (IRR)
1. Enter the cash flows using either of the methods described above under
Calculating Net Present Value.
2. Press fL.
The calculated value of IRR appears in the display and also is automatically
stored in the i register.
Note: Remember that the L function may take a significant amount of
time to produce an answer, during which the calculator displays running.
Example: The NPV calculated in the preceding example was positive,
indicating that the actual rate of return (that is, the IRR) was greater than the
13˝% used in the calculation. Find the IRR.
Assuming the cash flows are still stored in the calculator, we need only press
fL:
KeystrokesDisplay
fL
Note that the value calculated by L is the periodic rate of return. If the cash
flow periods are other than years (for example, months or quarters), you can
calculate the nominal annual rate of return by multiplying the periodic IRR by
the number of periods per year.
As noted above, the calculator may take several seconds or even minutes to
produce an answer for IRR. This is because the mathematical calculations for
13.72
IRR is 13.72%.
64 Section 4: Additional Financial Functions
finding IRR are extremely complex, involving a series of iterations – that is, a
series of successive calculations. In each iteration, the calculator uses an estimate
of IRR as the interest rate in a computation of NPV. The iterations are repeated
until the computed NPV reaches about zero.
16
The complex mathematical characteristics of the IRR computation have an
additional ramification: Depending on the magnitudes and signs of the cash
flows, the computation of IRR may have a single answer, multiple answers, a
negative answer or no answer.
17
For additional information regarding L, refer to Appendix C. For an
alternative method of calculating IRR, refer to Section 13.
Reviewing Cash Flow Entries
z To display a single cash flow amount, press :, then key in the number
of the register containing the cash flow amount to be displayed.
Alternatively, store the number of that cash flow amount (that is, the value
of j for the CF
z To review all the cash flow amounts, press :gK repeatedly. This
displays the cash flow amounts in reverse order – that is, beginning with
the final cash flow and proceeding to CF
z To display the number of times a cash flow amount occurs consecutively –
that is, to display the N
amount (that is, the value of j) in the n register, then press :ga.
z To review all the cash flow amounts together with the number of times
each cash flow amount occurs consecutively (that is, to review each CF
and Nj pair), press :ga:gK repeatedly. This displays N
followed by CFj beginning with the final cash flow amount and proceeding
to N
and CF0.
0
Note: Neither L nor l change the number in the n register. However,
each time :gK is pressed, the number in the n register is decreased
by 1. If this is done, or if you manually change the number in the n register
in order to display a single N
n register to the total number of cash flow amounts originally entered (not
including the amount of the initial investment CF
NPV and IRR calculations will give incorrect results; also, a review of cash
flow entries would begin with N
16.
In practice, because the complex mathematical calculations inside the calculator are done
with numbers rounded to 10 digits, NPV may never reach exactly zero. Nevertheless, the
interest rate that results in a very small NPV is very close to the actual IRR.
17.
In the case of multiple answers for IRR, the decision criteria listed on page 58 should be
modified accordingly.
desired) in the n register, then press :gK.
j
.
0
for a CFj – store the number of that cash flow
j
and/or CFj, be sure to reset the number in the
j
). If this is not done,
0
and CFn, where n is the number currently
n
j
j
Section 4: Additional Financial Functions65
in the n register.
For example, to display the fifth cash flow amount and the number of times that
amount occurs consecutively:
KeystrokesDisplay
:5
5n
:ga
7n
9,000.00
5.00
2.00
7.00
To display all the cash flow amounts and the number of times they occur
consecutively:
CF
5
Stores the value of j in the n
register.
N
5
Resets the number in the n register
to its original value.
KeystrokesDisplay
:ga
:gK
:ga
:gK
:ga
:gK
.
.
.
1.00
100,000.00
1.00
4,500.00
2.00
9,000.00
.
.
.
N
CF
N
CF
N
CF
7
7
6
6
5
5
.
.
.
:ga
:gK
:ga
:gK
7n
1.00
14,000.00
1.00
–79,000.00
7.00
N
1
CF
1
N
0
CF
0
Resets the number in the n register
to its original value.
66 Section 4: Additional Financial Functions
Changing Cash Flow Entries
z To change a cash flow amount:
1. Key the amount into the display.
2. Press ?.
3. Key in the number of the register containing the cash flow amount to be
changed.
z To change the number of times a cash flow amount occurs consecutively –
that is, to change the N
1. Store the number of that cash flow amount (that is, j) in the n register.
2. Key the number of times the cash flow amount occurs consecutively
into the display.
3. Press ga.
Note: If you change the number in the n register in order to change an N
be sure to reset the number in the n register to the total number of cash
flow amounts originally entered (not including the amount of the initial
investment CF
0
incorrect results.
Example 1: With the cash flows now stored in the calculator, change CF
$11,000 to $9,000, then calculate the new NPV for a 13½% return.
for a CFj:
j
). If this is not done, NPV and IRR calculations will give
2
from
,
j
KeystrokesDisplay
9000?2
13.5¼
fl
aThis step is necessary in this example because we have calculated IRR since the first
time we calculated NPV. The IRR calculation replaced the 13.5 we keyed into i before
calculating NPV with the result for IRR – 13.72.
9,000.00
13.50
–644.75
Since this NPV is negative, the investment would decrease the financial value of
the investor’s assets.
Example 2: Change N
from 2 to 4, then calculate the new NPV.
5
Stores the new CF2in R2.
a
Stores i
The new NPV.
Keystrokes Display
5n
4ga
7n
fl
5.00
4.00
7.00
–1,857.21
Stores j in the n register.
Stores the new N5.
Resets the number in the n register
to its original value.
The new NPV.
Bond Calculations
Section 4: Additional Financial Functions67
The HP 12C Platinum enables you to solve for bond price (and the interest
accrued since the last interest date) and the yield to maturity.
S calculations are done assuming a semiannual coupon payment and using an
actual/actual basis (such as for U.S. Treasury bonds and U.S. Treasury notes). In
accordance with market convention, prices are based on a redemption (par) value
of 100.
To calculate bond price and yield for a 30/360 bond (that is, using the basis of a
30-day month and a 360-day year – such as for municipal bonds, corporate
bonds, and state and local government bonds), and to calculate bond price for
bonds with an annual coupon payment, refer to Section 16: Bonds.
18
The E and
Bond Price
1. Enter the desired yield to maturity (as a percentage), using ¼.
2. Enter the annual coupon rate (as a percentage), using P.
3. Key in the settlement (purchase) date (as described on page 30), then press
\.
4. Key in the maturity (redemption) date.
5. Press fE.
The price is shown in the display and also is stored in the PV register. The
interest accrued since the last interest date is held inside the calculator: to display
the interest, press ~; to add the interest to the price, press +.
Example: What price should you pay on April 28, 2004 for a 6¾% U.S.
Treasury bond that matures on June 4, 2018, if you want a yield of 8¼%.
Assume that you normally express dates in the month-day-year format.
Keystrokes (RPN mode)Display
8.25¼
6.75P
gÕ
4.282004\
6.042018
fE
+
18.
All bond calculations are performed in accordance with. the Securities Industry Association’s
recommendations as contained in Spence, Graudenz, and Lynch, Standard Securities Calculation Methods, Securities Industry Association, New York, 1973.
8.25
6.75
6.75
4.28
6.042018
87.62
90.31
Enters yield to maturity.
Enters coupon rate.
Sets date format to month-day-year.
Enters settlement (purchase) date.
Enters maturity (redemption) date.
Bond price (as a percent of par).
Total price, including accrued
interest.
68 Section 4: Additional Financial Functions
Bond Yield
1. Enter the quoted price (as a percent of par), using $.
2. Enter the annual coupon rate (as a percentage), using P.
3. Key in the settlement (purchase) date, then press \.
4. Key in the maturity (redemption) date.
5. Press fS.
The yield to maturity is shown in the display and also is stored in the i register.
Note: Remember that the S function may take a significant amount of
time to produce an answer, during which the calculator displays running.
The HP 12C Platinum enables you to calculate depreciation and the remaining
depreciable value (book value minus salvage value) using the straight-line,
sum-of-the-years-digits, and declining-balance methods. To do so with any of
these methods:
1. Enter the original cost of the asset, using $.
2. Enter the salvage value of the asset, using M. If the salvage value is zero,
press 0M.
3. Enter the expected useful life of the asset (in years), using n.
4. If the declining-balance method is being used, enter the declining-balance
factor (as a percentage), using ¼. For example, 1¼ times the straight-line
rate – 125 percent declining-balance – would be entered as 125¼.
5. Key in the number of the year for which depreciation is to be calculated.
Section 4: Additional Financial Functions69
6. Press:
z fV for depreciation using the straight-line method.
z fÝ for depreciation using the sum-of-the-years digits method.
z f# for depreciation using the declining-balance method.
V, Ý, and # each place the amount of depreciation in the display. To
display the remaining depreciable value (the book value less the salvage value)
after the depreciation has been calculated, press ~.
Example: A metalworking machine, purchased for $10,000, is depreciated over
5 years. Its salvage value is estimated at $500. Find the depreciation and
remaining depreciable value for the first 3 years of the machine’s life using the
declining-balance method at double the straight-line rate (200 percent
declining-balance).
KeystrokesDisplay
10000$
500M
5n
200¼
1f#
~
2f#
~
3f#
~
10,000.00
500.00
5.00
200.00
4,000.00
5,500.00
2,400.00
3,100.00
1,440.00
1,660.00
Enters original cost.
Enters salvage value.
Enters expected useful life.
Enters declining-balance factor.
Depreciation in first year.
Remaining depreciable value after
first year.
Depreciation in second year.
Remaining depreciable value after
second year.
Depreciation in third year.
Remaining depreciable value after
third year.
To calculate depreciation and the remaining depreciable value when the
acquisition date of the asset does not coincide with the beginning of the fiscal
accounting year, refer to the procedures in Section 13. That section also includes
a procedure for depreciation calculations when changing from the
declining-balance method to the straight-line method, and a procedure for
calculating excess depreciation.
70 Section 5: Additional Operating Features
Section 5
Additional Operating Features
Continuous Memory
The calculator’s Continuous Memory contains the data storage registers, the
financial registers, the stack and LAST X registers, program memory, and status
information such as display format, date format, and payment mode. All
information in Continuous Memory is preserved even while the calculator is
turned off. Furthermore, information in Continuous Memory is preserved for a
short time when the batteries are removed, so that you can change the batteries
without losing your data and programs.
Continuous Memory may be reset if the calculator is dropped or otherwise
traumatized, or if power is interrupted. You can also manually reset Continuous
Memory as follows:
1. Turn the calculator off.
2. Hold down the - key, and press ;.
When Continuous Memory is reset:
z All registers are cleared.
z Program memory consists of eight program lines, each containing the
instruction g(000.
z Display format is set to the standard format with two decimal places.
z Date format is set to month-day-year.
z Payment mode is set to End.
Whenever Continuous Memory has been reset, the display will show Pr Error.
Pressing any key will clear this message from the display.
The Display
Status Indicators
Eight indicators that appear along the bottom of the display signify the status of
the calculator for certain operations. These status indicators are described
elsewhere in this handbook where the relevant operation is discussed.
RPN ALGfgBEGIN D.MYCPRGM
Section 5: Additional Operating Features71
Number Display Formats
When the calculator is first turned on after coming from the factory or after
Continuous Memory has been reset, answers are displayed with two decimal
places.
Keystrokes (RPN mode)Display
19.8745632\
5-
Although you see only two decimal places, all calculations in your HP 12C
Platinum are performed with full 10-digit numbers.
19.87
14.87
Youseeonlythesedigits...
...butthesedigitsarealsopresentinternally
When only two decimal places are displayed, numbers are rounded to two
decimal places: if the third digit is 5 through 9, the second digit is increased by
one; if the third digit is 0 through 4, the second digit is not affected. Rounding
occurs regardless of how many decimal places are displayed.
Several options are provided for controlling how numbers appear in the display.
But regardless of which display format or how many displayed decimal places
you specify, the number inside the calculator – which appears altered in the
display – is not altered unless you use the B, !, V, Ý, or #
functions.
Standard Display Format. The number 14.87 now in your calculator is
currently being displayed in the standard display format with two decimal places
shown. To display a different number of decimal places, press f followed by a
digit key (0 through 9) specifying the number of decimal places. In the following
examples, notice how the displayed form of the number inside the calculator –
14.87456320 – is rounded to the specified number of digits.
72 Section 5: Additional Operating Features
KeystrokesDisplay
f4
f1
f0
f9
The standard display format, plus the specified number of decimal places,
remain in effect until you change them; they are not reset each time the
calculator is turned on. However, if Continuous Memory is reset, when the
calculator is next turned on numbers will be displayed in the standard display
format with two decimal places shown.
If a calculated answer is either too small or too large to be displayed in the
standard display format, the display format automatically switches to scientific
notation (described below). The display returns to the standard display format
for all numbers that can be displayed in that format.
14.8746
14.9
15.
14.87456320
Although nine decimal places were
specified after f, only eight are
displayed since the display can
show a total of only 10 digits.
Scientific Notation Display Format
7-digitmantissaExponentof10
SignofexponentSignofmantissa
In scientific notation, a number is displayed with its mantissa at the left and a
two-digit exponent at the right. The mantissa is simply the first seven digits in
the number, and has a single, nonzero digit to the left of the decimal point. The
exponent is simply how many decimal places you would move the decimal point
in the mantissa before writing down the number in standard format. If the
exponent is negative (that is, there is a minus sign between it and the mantissa),
the decimal point should be moved to the left; this occurs for any number less
than 1. If the exponent is positive (that is, there is a blank space between it and
the mantissa), the decimal point should be moved to the right; this occurs for any
number greater than or equal to 1.
Section 5: Additional Operating Features73
To set the display format to scientific notation, press f.. For example
(assuming the display still shows 14.87456320 from the preceding example):
KeystrokesDisplay
f.
The exponent in this example indicates that the decimal point should be moved
one decimal place to the right, giving the number 14.87456, which is the first
seven digits of the number previously in the display.
To set the display back to standard display format, press f followed by the
desired number of decimal places. Scientific notation display format remains in
effect until you change to the standard display format; it is not reset each time the
calculator is turned on. However, if Continuous Memory is reset, when the
calculator is next turned on the standard display format, with two decimal places,
will be used.
Mantissa Display Format. Because both the standard display format and
scientific notation display format often show only a few digits of a number, you
may occasionally want to see all 10 digits – the full mantissa – of the number
inside the calculator. To do so, press fCLEAR X and hold down the X
key. The display will show all 10 digits of the number as long as you hold down
the X key; after you release the key, the number will again be displayed in the
current display format. For instance, if the display still contains the result from
the preceding example:
1.487456 01
KeystrokesDisplay
fCLEAR X
f2
1487456320
1.487456 01
14.87
All 10 digits of the number inside
the calculator.
Display returns to its former
contents when the X key is
released.
Returns display to standard format.
Special Displays
Running. Certain functions and many programs may take several seconds or
more to produce an answer. During these calculations, the word running flashes
in the display to let you know that the calculator is running.
Overflow and Underflow. If a calculation results in a number whose magnitude
is greater than 9.999999999 × 10
displays 9.999999 99 (if the number is positive) or –9.999999 99 (if the
number is negative).
99
, the calculation is halted and the calculator
74 Section 5: Additional Operating Features
If a calculation results in a number whose magnitude is less than 10
calculation is not halted, but the value 0 is used for that number in subsequent
calculations.
Errors. If you attempt an improper operation – such as division by zero – the
calculator will display the word Error followed by a digit (0 through 9). To clear
the Error display, press any key. This does not execute that key’s function, but
does restore the calculator to its condition before the improper operation was
attempted. Refer to Appendix D for a list of error conditions.
Pr Error. If power to the calculator is interrupted, the calculator will display Pr
Error when next turned on. This indicates that Continuous Memory – which
contains all data, program, and status information – has been reset.
.99
, the
The ~ Key
Suppose you need to subtract $25.83 from $144.25, and you (mistakenly) key in
25.83, press \, then key in 144.25. But then you realize that when written
down on paper, the desired calculation reads 144.25 – 25.83, so that you have
unfortunately keyed in the second number first. To correct this mistake, merely
exchange the first and second numbers by pressing ~, the exchange key.
Keystrokes (RPN mode)Display
25.83\144.25
~
-
144.25
25.83
118.42
Oops! You mistakenly keyed in the
second number first.
Exchanges the first and second
numbers. The first number keyed in
is now in the display.
The answer is obtained by pressing
the operation key.
The ~ key is also useful for checking the first number entered to make sure
you keyed it in correctly. Before pressing the operation key, however, you should
press ~ again to return the second number entered to the display. Regardless
of how many times you press ~, the calculator considers the number in the
display to be the second number entered.
The F Key
Occasionally you may want to recall to the display the number that was there
before an operation was performed. (This is useful for doing arithmetic
calculations with constants and for recovering from errors in keying in numbers.)
To do so, press gF (last x).
Section 5: Additional Operating Features75
Arithmetic Calculations With Constants
Example: At Permex Pipes a certain pipe fitting is packaged in quantities of 15,
75, and 250. If the cost per fitting is $4.38, calculate the cost of each package.
Keystrokes (RPN mode)Display
15\
4.38
§
75
gF
§
250
gF
§
Another method for doing arithmetic calculations with constants is described on
page 173.
15.00
4.38
65.70
75.
4.38
328.50
250.
4.38
1,095.00
Keys first quantity into calculator.
Keys unit cost into display.
Cost of a package of 15.
Keys second quantity into display.
Recalls unit cost – which was last
number in display before § was
pressed – into display.
Cost of a package of 75.
Keys third quantity into display.
Recalls unit cost into display again.
Cost of a package of 250.
Recovering From Errors in Digit Entry
Example: Suppose you want to divide the total annual production for one of
your firm’s products (429,000) by the number of retail outlets (987) in order to
calculate the average number distributed by each outlet. Unfortunately, you
mistakenly key in the number of outlets as 9987 rather than as 987. It’s easy to
correct:
Keystrokes (RPN mode)Display
429000\
9987
z
gF
429000\
987z
429,000.00
9,987.
42.96
9,987.00
429,000.00
434.65
You haven’t noticed your mistake
yet.
About 43 products per outlet – but
that seems too low!
Recalls to the display the number
that was there before you press z.
You see that you keyed it in wrong.
Begins the problem over.
The correct answer.
Section 6
Statistics Functions
Accumulating Statistics
The HP 12C Platinum can perform one- or two-variable statistical calculations.
The data is entered into the calculator using the _ key, which automatically
calculates and stores statistics of the data into storage registers R
(These registers are therefore referred to as the “statistics registers.”)
Before beginning to accumulate statistics for a new set of data, you should clear
the statistics registers by pressing fCLEAR².
19
In one-variable statistical calculations, to enter each data point – referred to as an
“x-value” – key the x-value into the display, then press _.
In two-variable statistical calculations, to enter each data pair – referred to as the
“x- and y-values”:
1. Key the y-value into the display.
2. Press \.
3. Key the x-value into the display.
4. Press _.
Each time you press _, the calculator does the following:
z The number in R
is increased by 1, and the result is copied into the
1
display.
z The x-value is added to the number in R
z The square of the x-value is added to the number in R
z The y-value is added to the number in R
z The square of the y-value is added to the number in R
z The product of the x- and y-values is added to the number in R
.
2
.
4
The table below shows where the accumulated statistics are stored.
.
3
.
5
, through R6.
1
.
6
19.
This also clears the stack registers and the display.
76
Section 6: Statistics Functions77
RegisterStatistic
R1 (and display)n: number of data pairs accumulated.
R
2
R
3
Σx: summation of x-values.
Σx2: summation of squares of
x-values.
R
4
R
5
R
6
Σy: summation of y-values.
Σy2 summation of squares of y-values.
Σxy: summation of products of
x-values and y-values.
Correcting Accumulated Statistics
If you discover you have entered data incorrectly, the accumulated statistics can
easily be corrected:
z If the incorrect data point or data pair has just been entered and _ has
been pressed, press gFg^.
z If the incorrect data point or data pair is not the most recent one entered,
key in the incorrect data point or data pair again as if it were new, but press
g^ instead of _.
These operations cancel the effect of the incorrect data point or data pair. You
can then enter the data correctly, using _, just as if it were new.
Mean
Pressing gÖ calculates the means (arithmetic averages) of the x-values ( )
and of the y-values ( ). The mean of the x-values appears in the display after Ö
y
x
is pressed; to display the mean of the y-values, press ~.
Example: A survey of seven salespersons in your company reveals that they
work the following hours a week and sell the following dollar volumes each
month. How many hours does the average salesperson work each week? How
much does the average salesperson sell each month?
78 Section 6: Statistics Functions
SalespersonHours/WeekHours/Week
132$17,000
240$25,000
345$26,000
440$20,000
538$21,000
650$28,000
735$15,000
To find the average workweek and sales of this sample:
KeystrokesDisplay
fCLEAR²
32\
17000_
40\
25000_
45\
26000_
40\
20000_
38\
21000_
50\
28000_
35\
15000_
gÖ
~
0.00
32.00
1.00
40.00
2.00
45.00
3.00
40.00
4.00
38.00
5.00
50.00
6.00
35.00
7.00
21,714.29
40.00
Clears statistics registers.
First entry.
Second entry.
Third entry.
Fourth entry.
Fifth entry.
Sixth entry.
Total number of entries in the
sample.
Mean dollar sales per month ( ).
Mean workweek in hours ( ).
x
y
Standard Deviation
Pressing gv calculates the standard deviation of the x-values (sx) and of the
y-values (s
dispersion around the mean.) The standard deviation of the x-values appears in
the display after v is pressed; to display the standard deviation of the y-values,
press ~.
). (The standard deviation of a set of data is a measure of the
y
Section 6: Statistics Functions79
Example: To calculate the standard deviations of the x-values and of the
y-values from the preceding example:
KeystrokesDisplay
gv
~
4,820.59
6.03
Standard deviation of sales.
Standard deviation of hours worked.
The formulas used in the HP 12C Platinum for calculating s
, and sy give best
x
estimates of the population standard deviation based on a sample of the
population. Thus, current statistical convention calls them sample standard
deviations. So we have assumed that the seven salespersons are a sample of the
population of all salespersons, and our formulas derive best estimates of the
population from the sample.
What if the seven salespersons constituted the whole population of salespersons.
Then we wouldn’t need to estimate the population standard deviation. We can
find the true population standard deviation (σ) when the data set equals the total
population, using the following keystrokes.
20
KeystrokesDisplay
gÖ
_
gv
~
21,714.29
8.00
4,463.00
5.58
To continue summing data pairs, press gÖg^ before entering more data.
Mean (dollars)
Number of entries + 1.
σ
x
σ
y
Linear Estimation
With two-variable statistical data accumulated in the statistics registers, you can
estimate a new y-value ( ) given a new x-value, and estimate a new x-value ( )
y
ˆ
given a new y-value.
To calculate :
y
ˆ
1. Key in a new x-value.
2. Press gR.
x
ˆ
To calculate :
x
ˆ
1. Key in a new y-value.
2. Press gQ.
20.
It turns out that if you sum the mean of the population into the set itself and find the new s,
computed using the formulas on page 192, that s will be the population standard deviation, σ,
of the original set.
80 Section 6: Statistics Functions
Example: Using the accumulated statistics from the preceding problem,
estimate the amount of sales delivered by a new salesperson working 48 hours
per week.
KeystrokesDisplay
48gQ
The reliability of a linear estimate depends upon how closely the data pairs
would, if plotted on a graph, lie in a straight line. The usual measure of this
reliability is the correlation coefficient, r. This quantity is automatically
calculated whenever or is calculated; to display it, press ~. A correlation
coefficient close to 1 or –1 indicates that the data pairs lie very close to a straight
line. On the other hand, a correlation coefficient close to 0 indicates that the data
pairs do not lie closely to a straight line; and a linear estimate using this data
would not be very reliable.
Example: Check the reliability of the linear estimate in the preceding example
by displaying the correlation coefficient.
28,818.93
yˆx
ˆ
Estimated sales for a 48 hour
workweek.
KeystrokesDisplay
~
0.90
The correlation coefficient is close
to 1, so the sales calculated in the
preceding example is a good
estimate.
To graph the regression line, calculate the coefficients of the linear equation
y = A + Bx.
1. Press 0gR to compute the y-intercept (A).
2. Press 1gR~d~- to compute the slope of the line (B).
Example: Compute the slope and intercept of the regression line in the
preceding example.
Keystrokes (RPN mode) Display
0gR
1 gR~d~-
The equation that describes the regression line is:
15.55
0.001
y = 15.55 + 0.001x
y-intercept (A); projected value for
x = 0.
Slope of the line (B); indicates the
change in the projected values
caused by an incremental change in
the x value.
Section 6: Statistics Functions81
Weighted Mean
You can compute the weighted mean of a set of numbers if you know the
corresponding weights of the items in question.
1. Press fCLEAR².
2. Key in the value of the item and press \, then key in its weight and
press _. Key in the second item’s value, press \, key in the second
weight, and press _. Continue until you have entered all the values of the
items and their corresponding weights. The rule for entering the data is
“item \ weight _.”
3. Press gh to calculate the weighted mean of the items.
Example: Suppose that you stop during a vacation drive to purchase gasoline at
four stations as follows: 15 gallons at $1.16 per gallon, 7 gallons at $1.24 per
gallon, 10 gallons at $1.20 per gallon, and 17 gallons at $1.18 per gallon. You
want to find the average cost per gallon of gasoline purchased. If you purchased
the same quantity at each station, you could determine the simple arithmetic
average or mean using the Ö key. But since you know the value of the item
(gasoline) and its corresponding weight (number of gallons purchased), use the
h key to find the weighted mean:
KeystrokesDisplay
fCLEAR²
1.16\15_
1.24\7_
1.20\10_
1.18\17_
gh
0.00
1.00
2.00
3.00
4.00
1.19
Clears statistics registers.
First item and weight.
Second item and weight.
Third item and weight.
Fourth item and weight.
Weighted mean cost per gallon.
A procedure for calculating the standard deviation and standard error (as well as
the mean) of weighted or grouped data is included in the HP 12C Platinum Solutions Handbook.
Section 7
Mathematics and
Number-Alteration Functions
The HP 12C Platinum provides several keys for mathematical functions and for
altering, numbers. These functions are useful for specialized financial
calculations as well as for general mathematics calculations.
One-Number Functions
Most of the mathematics functions require that only one number be in the
calculator (that is, the number in the display) before the function key is pressed.
Pressing the function key then replaces the number in the display by the result.
Reciprocal. Pressing y calculates the reciprocal of the number in the display –
that is, it divides 1 by the number in the display.
Square. Pressing g’ calculates the square of the number in the display.
Square Root. Pressing gr calculates the square root of the number in the
display.
Logarithm. Pressing g¿ calculates the natural logarithm (that is, the
logarithm to the base e) of the number in the display. To calculate the common
logarithm (that is, the logarithm to the base 10) of the number in the display,
calculate the natural logarithm, then press 10g¿z.
Exponential. Pressing g> calculates the exponential of the number in the
display – that is, it raises the base e to the number in the display.
Factorial. Pressing ge calculates the factorial of the number in the display –
that is, it calculates the product of the integers from 1 to n, where n is the number
in the display.
Round. The display format specifies to how many decimal places a number
inside the calculator is rounded when it appears in the display; but the display
format alone does not affect the number itself inside the calculator. Pressing
fB, however, changes the number inside the calculator to match its
displayed version. Thus, to round a number in the display to a given number of
decimal places, temporarily set the display format (as described on page 71) to
show the desired number of decimal places, then press fB.
82
Section 7: Mathematics and Number-Alteration Functions83
Integer. Pressing gÑ replaces the number in the display by its integer
portion – that is, it replaces each digit to the right of the decimal point by 0. The
number is changed inside the calculator as well as in the display. The original
number can be recalled to the display by pressing gF.
Fractional. Pressing gT replaces the number in the display by its fractional
portion – that is, it replaces all digits to the left of the decimal point by 0. Like
Ñ, T changes the number inside the calculator as well as its displayed
version. The original number can be recalled to the display by pressing gF.
All of the above functions are used basically in the same way. For example, to
find the reciprocal of 0.258:
Keystrokes Display
.258
y
Any of the above functions can be done with a number in the display resulting
from a previous calculation, as well as with a number you have just keyed in.
0.258
3.88
Keys the number into the display.
The reciprocal of 0.258, the original
number.
Keystrokes (RPN mode)Display
fCLEAR X
fB
fX
gÑ
gF
gT
3875968992
3.88
3.88
3880000000
3.88
3.00
3.88
0.88
Displays all 10 digits of the number
inside the calculator.
Display returns to normal format
when X key is released.
The number now in the display
appears the same as before, but …
Displaying all 10 digits of the
number inside the calculator shows
B has changed the number to
match its displayed version.
Display returns to normal format.
The integer portion of the number
previously displayed.
Recalls the original number to the
display.
The fractional portion of the
number previously displayed.
84 Section 7: Mathematics and Number-Alteration Functions
The Power Function
Pressing q calculates a power of a number – that is, yx. Like the arithmetic
function +, q requires two numbers:
1. Key in the base number (which is designated by the y on the key).
2. Press \ to separate the second number (the exponent) from the first (the
base).
3. Key in the exponent (which is designated by the x on the key).
4. Press q to calculate the power.
To CalculateKeystrokes (RPN mode)Display
1.4
2
–1.4
2
(–2)
3
2
3
or 2
2\1.4q
2\1.4Þq
2Þ\3q
1/3
2\3yq
2.64
0.38
–8.00
1.26
Part II
Programming
Section 8
Programming Basics
Why Use Programs?
A program is simply a sequence of keystrokes that is stored in the calculator.
Whenever you have to calculate with the same sequence of keystrokes several
times, you can save a great deal of time by incorporating these keystrokes in a
program. Instead of pressing all the keys each time, you press just one key to
start the program: the calculator does the rest automatically!
Creating a Program
While in programming made, before pressing steps, users need to creating a
program consists simply of writing the program, then storing it:
1. Write down the sequence of keystrokes that you would use to calculate the
quantity or quantities desired.
2. Press fs to set the calculator to Program mode. When the calculator
is in Program mode, functions are not executed when they are keyed in, but
instead are stored inside the calculator. The PRGM status indicator in the
display is lit when the calculator is in Program mode.
3. Press fCLEARÎ to erase any previous programs that may be stored
inside the calculator. If you want to create a new program without erasing a
program already stored, skip this step and proceed as described in Section
11, Multiple Programs.
4. Select the mode you want to use (by pressing f] or f[).
Note: Programs or steps created and saved in RPN mode can only be
executed in RPN mode, and programs or steps created and saved in ALG
mode can only be executed in ALG mode. (You can also create steps in
your program to switch to the appropriate mode.)
5. Key in the sequence of keystrokes that you wrote down in step 1. Skip the
beginning keystrokes that enter data, which would differ each time the
program is used.
Example: Your office supplies dealer is selling selected stock at 25% off. Create
a program that calculates the net cost of an item after the discount is subtracted
and the $5 handling charge is added.
First, we’ll manually calculate the net cost of an item listing for $200.
86
Section 8: Programming Basics87
Keystrokes (RPN mode)Display
200
\
25b
-
5
+
Next, set the calculator to Program mode and erase any program(s) already
stored:
200.
200.00
50.00
150.00
5.
155.00
Keys in cost of item.
Separates cost of item from
percentage to be keyed in next.
Amount of discount.
Price less discount.
Handling charge.
Net cost (price less discount plus
handling charge).
Keystrokes (RPN mode)Display
fs
fCLEARÎ
Finally, press the keys that we used above to solve the problem manually. Do not
key in 200; this number will vary each time the program is used. Don’t be
concerned right now about what appears in the display as you press the keys;
we’ll discuss that later in this section.
000,
000,
Sets calculator to Program mode.
Clears program(s).
Keystrokes (RPN mode)Display
\
2
5
b
-
5
+
001,36
002,2
003,5
004,25
005,30
006,5
007,40
Running a Program
To run (sometimes called “execute”) a program:
1. Press fs to set the calculator back to Run mode. If the calculator is
already in Run mode (that is, the PRGM status indicator in the display is
not lit), skip this step.
2. Key any required data into the calculator, just as if you were calculating
manually. When a program is run, it uses the data already keyed into the
display and the registers inside the calculator.
3. Press t to begin program execution.
88 Section 8: Programming Basics
Example: Run the program created above to calculate the net cost of a
typewriter listing for $625 and an executive chair listing for $159.
Keystrokes (RPN mode)Display
fs
625
t
159
t
That’s all there is to creating and running simple programs! But if you want to
use programs frequently, you’ll want to know more about programming – such
as how to check what keystrokes are stored in program memory, how many
keystrokes can be stored in program memory, how to correct or otherwise
modify programs, how to skip keystrokes when running a program, and so on.
Before you can understand these aspects of programming, we need to briefly
discuss how keystrokes are treated by the calculator when they are stored in
Program mode and when they are executed in Run mode.
155.00
625.
473.75
159.
124.25
Sets calculator to Run mode.
Display shows number previously
calculated.
Keys in price of typewriter.
Net cost of typewriter.
Keys in list price of chair.
Net cost of chair.
Program Memory
Keystrokes entered into the calculator in Program mode are stored in program
memory. Each digit, decimal point, or function key is called an instruction and is
stored in one line of program memory – usually referred to simply as a program
line. Keystroke sequences beginning with the f, g, ?, :, and i
prefix keys are considered to comprise a complete instruction and are stored in
only one program line.
When a program is run, each instruction in program memory is executed – that
is, the keystroke in that program line is performed, just as if you were pressing
the key manually – beginning with the current line in program memory and
proceeding sequentially with the higher-numbered program lines.
Whenever the calculator is in Program mode (that is, whenever the PRGM status
indicator in the display is lit), the display shows information about the program
line to which the calculator is currently set. At the left of the display is the
number of the program line within program memory. The remaining digits in the
display comprise a code that indicates what instruction has been stored in that
program line. No code is shown for program line 000, since no regular
instruction is stored there.
Section 8: Programming Basics89
Identifying Instructions in Program Lines
Each key on the HP 12C Platinum keyboard – except for the digit keys 0 through
9 – is identified by a two-digit “keycode” that corresponds to the key’s position
on the keyboard. The first digit in the keycode is the number of the key row,
counting from row 1 at the top; the second digit is the number of the key in that
row, counting from 1 for the first key in the row through 9 for the ninth key in the
row and 0 for the tenth key in the row. The keycode for each digit key is simply
the digit on the key. Thus, when you keyed the instruction b into program
memory, the calculator displayed
004, 25
This indicates that the key for the instruction in program line 004 is in the second
row on the keyboard and is the fifth key in that row: the b key. When you
keyed the instruction + into program memory, the calculator displayed
007, 40
This indicates that the key for the instruction in program line 007 is in the fourth
row on the keyboard and is the tenth key in that row: the + key. When you
keyed the digit 5 into program memory, the keycode displayed was only the
digit 5.
hp 12c platinum
financial calculator
2
=
Since keystroke sequences beginning with f, g, ?, :, and i are
stored in only one program line, the display of that line would show the keycodes
for all the keys in the keystroke sequence.
InstructionKeycode
gÒ
?=1
gi000
nnn,43 26
nnn,44 40 1
nnn,43,33,000
90 Section 8: Programming Basics
Displaying Program Lines
Pressing fs to set the calculator from Run mode to Program mode displays
the line number and keycode for the program line to which the calculator is
currently set.
Occasionally you’ll want to check several or all of the instructions stored in
program memory. The HP 12C Platinum enables you to review program
instructions either forward or backward through program memory:
z Pressing Ê (single step) while the calculator is in Program mode
advances the calculator to the next line in program memory, then displays
that line number and the keycode of the instruction stored there.
z Pressing gÜ (back step) while the calculator is in Program mode sets
the calculator back to the previous line in program memory, then displays
that line number and the keycode of the instruction stored there.
For example, to display the first two lines of the program now stored in program
memory, set the calculator to Program mode and press Ê twice:
KeystrokesDisplay
fs
Ê
Ê
000,
001,36
002,2
Sets calculator to Program
mode and displays current line
of program memory
Program line 001: \
Program line 002: digit 2.
Pressing gÜ does the reverse:
KeystrokesDisplay
gÜ
gÜ
If either the Ê key or the Ü key is held down, the calculator displays all of
the lines in program memory. Press Ê again now, but this time hold it down
until program line 007 is displayed.
001,36
000,
Program line 001.
Program line 000.
KeystrokesDisplay
Ê
(Release Ê)
001,36
.
.
.
007,40
Program line 001
.
.
.
Program line 007
Section 8: Programming Basics91
Program line 007 contains the last instruction you keyed into program memory.
However, if you press Ê again, you’ll see that this is not the last line stored in
program memory:
KeystrokesDisplay
Ê
As you should now be able to tell from the keycodes displayed, the instruction in
program line 008 is gi000.
008,43,33,000
Program line 008
The i000 Instruction and Program Line 000
Whenever you run the program now stored in program memory, the calculator
executes the instruction in line 008 after executing the seven instructions you
keyed in. This i000 instruction – as its name implies – tells the calculator to
“go to” program line 000 and execute the instruction in that line. Although line
000 does not contain a regular instruction, it does contain a “hidden” instruction
that tells the calculator to halt program execution. Thus, after each time the
program is run, the calculator automatically goes to program line 000 and halts,
ready for you to key in new data and run the program again. (The calculator is
also automatically set to program line 000 when you press fs to set the
calculator from Program mode to Run mode.)
The i000 instruction was already stored in line 008 – in fact, in all program
lines – before you keyed in the program. If no instructions have been keyed into
program memory, if Continuous Memory is reset, or if fCLEARÎ is
pressed (in Program mode), the instruction i000 is automatically stored in
program lines 001 through 008. As you key each instruction into program
memory, it replaces the i000 instruction in that program line.
If your program should consist of exactly eight instructions, there would be no
i000 instructions remaining at the end of program memory. Nevertheless,
after such a program is executed the calculator automatically returns to program
line 000 and halts, just as if there were a i000 instruction following the
program.
If you key in more than eight instructions, program memory automatically
expands to accommodate the additional instructions.
Expanding Program Memory
If no instructions have been keyed into program memory, if Continuous Memory
has been reset, or if fCLEARÎ has been pressed (in Program mode),
92 Section 8: Programming Basics
program memory consists of 8 program lines, and there are 20 storage registers
available for storage of data.
ProgramMemoryStorageRegisters
As you key in a 310th instruction, storage register R
is automatically converted
0.9
into seven new lines of program memory. The instruction you key in is stored in
program line 310, and the instruction i000 is automatically stored in
program lines 311 through 316.
ProgramMemoryStorageRegisters
310
311
312313314315
316
Program memory is automatically expanded like this whenever another seven
instructions have been keyed into program memory – that is, when you key an
instruction into program line 317, 324, 331 etc. In each case, the additional
program lines made available are converted, seven lines at a time, from the last
available data storage register (whether or not data has been stored in that
register; if it has, it will be lost). Furthermore, the six new program lines
(following the 317th, 324th etc.) will each contain the instruction i000.
Section 8: Programming Basics93
To determine at any time how many program lines (including those containing
i000) are currently in program memory and how many storage registers are
currently available for conversion to program lines or for data storage, press
gN (memory). The calculator will respond with a display like the following:
AllocatedprogramlinesAvailablestorageregisters
Up to 400 instructions can be stored in program memory. Doing so would
require the conversion of 56 data storage registers (because 400 = 8 + [56 × 7]),
leaving 7 storage registers – R
through R6 – available for data storage.
0
If you find yourself creating long programs, you should create your programs so
that they don’t use up program lines unnecessarily, since program memory is
limited to 400 program lines. One way to minimize program length is to replace
numbers consisting of more than just one digit – like the number 25 in lines 002
and 003 of the program keyed in above – by a : instruction, and then storing
the number in the designated storage register before running the program. In this
case, this would save one program line, since the : instruction requires only
one program line, not two as are required by the number 25. Of course, doing so
uses up data storage registers that you might want to save for other data. As in
many business and financial decisions, there is a trade off involved; here it is
between program lines and data storage registers.
Setting the Calculator to a Particular Program Line
There will be occasions when you’ll want to set the calculator directly to a
particular program line – such as when you’re storing a second program in
program memory or when you’re modifying an existing program. Although you
can set the calculator to any line by using Ê as described above, you can do so
more quickly as follows:
z With the calculator in Program mode, pressing gi. followed by
three digit keys sets the calculator to the program line specified by the digit
keys, and then displays that line number and the keycode of the instruction
stored there.
z With the calculator in Run mode, pressing gi followed by three digit
keys sets the calculator to the program line specified by the digit keys.
Since the calculator is not in Program mode, the line number and keycode
are not displayed.
The decimal point is not necessary if the calculator is in Run mode, but it is
necessary if the calculator is in Program mode.
94 Section 8: Programming Basics
For example, assuming the calculator is still in Program mode, you can set it to
program line 000 as follows:
KeystrokesDisplay
gi.000
000,
Program line 000
Executing a Program One Line at a Time
Pressing Ê repeatedly with the calculator in Program mode (as described
earlier) enables you to verify that the program you have stored is identical to the
program you wrote – that is, to verify that you have keyed the instructions in
correctly. However, this does not ensure that the program you wrote calculates
the desired results correctly: even programs created by the most experienced
programmers often do not work correctly when they are first written.
To help you verify that your program works correctly, you can execute the
program one line at a time, using the Ê key. Pressing Ê while the calculator
is in Run mode advances the calculator to the next line in program memory, then
displays that line’s number and the keycode of the instruction stored there, just as
in Program mode. In Run mode, however, when the Ê key is released the
instruction in the program line just displayed is executed and the display then
shows the result of executing that line.
For example, to execute the program stored in the calculator one line at a time:
Keystrokes
(RPN mode)
fs
625
Ê
Ê
Ê
Ê
Display
124.25
625.
001,36
625.00
002,2
2.
003,5
25.
004,25
Sets calculator to Run mode and
to line 000 in program memory.
(Display shown assumes results
remain from previous
calculation.)
Keys in price of typewriter.
Program line 001: \
Result of executing program line
001.
Program line 002: 2.
Result of executing program line
002.
Program line 003: 5.
Result of executing program line
003.
Program line 004: b
Section 8: Programming Basics95
Keystrokes
(RPN mode)
Ê
Ê
Ê
Pressing gÜ while the calculator is in Run mode sets the calculator to the
previous line in program memory, then displays that line’s number and the
keycode of the instruction stored there, just as in Program mode. In Run mode,
however, when the Ü key is released the display again shows the same
number as it did before gÜ was pressed: no instruction in program memory
is executed.
Display
156.25
005,30
468.75
006,5
5.
007,40
473.75
Result of executing program line
004.
Program line 005: Result of executing program line
005.
Program line 006: 5
Result of executing program line
006.
Program line 007: +
Result of executing program line
007 (the last line of the program).
Interrupting Program Execution
Occasionally you’ll want a program to stop executing so that you can see an
intermediate result or enter new data. The HP 12C Platinum provides two
functions for doing so: u (pause) and t (run/stop).
Pausing During Program Execution
When a running program executes a u instruction, program execution halts
for about 1 second, then resumes. During the pause, the calculator displays the
last result calculated before the u instruction was executed.
If you press any key during a pause, program execution is halted indefinitely. To
resume program execution at the program line following that containing the u
instruction, press t.
Example: Create a program that calculates the entries in the AMOUNT, TAX,
and TOTAL columns for each item on the jewelry distributor’s invoice shown on
the next page, and also calculates the total in each of these columns for all items
on the invoice. Assume the sales tax is 6¾%.
To conserve lines of program memory, instead of keying in the tax rate before
the b instruction we’ll store it in register R
instruction. Before storing the program in program memory, we’ll calculate the
and recall it before the b
0
96 Section 8: Programming Basics
required amounts for the first item on the invoice manually. The keystroke
sequence will use storage register arithmetic (described on page 25) in registers
, R2, and R3 to calculate the column sums. Since these registers are cleared
R
1
when fCLEAR² is pressed, we’ll press those keys before beginning the
manual calculation – and also later, before running the program – to ensure that
the column sums are “initialized” to zero. (Pressing fCLEARH would clear
registers R
through R3, but would also clear R0, which will contain the tax rate.)
Pressing the gu keys is not necessary when we do the calculations
manually, since in Run mode the result of every intermediate calculation is
displayed automatically; but we’ll include u instructions in the program so
that the intermediate results AMOUNT and TAX are automatically displayed
when the program is executed.
Section 8: Programming Basics97
Keystrokes
(RPN mode)
6.75?0
fCLEAR²
13
\
68.5
§
?+1
:0
b
?+2
+
?+3
Now, we’ll store the program in program memory. Do not key in the quantity and
cost of each item; these numbers will vary each time the program is run.
Keystrokes
(RPN mode)
fs
fCLEARÎ
§
gu
?+1
:0
b
gu
?+2
+
?+3
Display
6.75
0.00
13.
13.00
68.5
890.50
890.50
6.75
60.11
60.11
950.61
950.61
Display
000,
000,
001,20
002,43 31
003,44 40 1
004,45 0
005,25
006,43 31
007,44 40 2
008,40
009,44 40 3
Stores tax rate in R0.
Clears the registers in R1 through
.
R
6
Keys in quantity of item.
Separates quantity of item from
cost of item to be keyed in next.
Keys in cost of item.
AMOUNT.
Adds AMOUNT to sum of
AMOUNT entries in register R
Recalls tax rate to display.
TAX.
Adds TAX to sum of TAX entries
in register R
TOTAL.
Adds TOTAL to sum of TOTAL
entries in register R
Sets calculator to Program mode.
Clears program memory.
Pauses to display AMOUNT.
Pauses to display TAX.
.
2
.
3
1
.
98 Section 8: Programming Basics
Now, to run the program:
Keystrokes
(RPN mode)
fs
fCLEAR²
6.75?0Stores tax rate.
13\68.5
t
18\72.9
t
24\85
t
5\345
t
:1
:2
:3
Display
950.61
0.00
68.5
890.50
60.11
950.61
72.9
1,312.20
88.57
1,400.77
85.
2,040.00
137.70
2,177.70
345.
1,725.00
116.44
1,841.44
5,967.70
402.82
6,370.52
Sets calculator to Run mode.
Clears registers R1– R6.
Enters quantity and price of first
item on invoice.
AMOUNT for first item.
TAX for first item.
TOTAL for first item.
Enters quantity and price of
second item on invoice.
AMOUNT for second item.
TAX for second item.
TOTAL for second item.
Enters quantity and price of third
item on invoice.
AMOUNT for third item.
TAX for third item.
TOTAL for third item.
Enters quantity and price of
fourth item on invoice.
AMOUNT for fourth item.
TAX for fourth item.
TOTAL for fourth item.
Sum of AMOUNT column.
Sum of TAX column.
Sum of TOTAL column.
If the duration of the pause is not long enough to write down the number
displayed, you can prolong it by using more than one u instruction.
Alternatively, you can have the program automatically stop as described next.
Stopping Program Execution
Stopping Program Execution Automatically. Program execution is
automatically halted when the program executes a t instruction. To resume
executing the program from the program line at which execution was halted,
press t.
Section 8: Programming Basics99
Example: Replace the program above by one containing t instructions
instead of u instructions.
Keystrokes
(RPN mode)
fs
fCLEARÎ
§
t
?+1
:0
b
t
?+2
+
?+3
fs
fCLEAR²
13\68.5
t
t
t
18\72.9
t
t
t
24\85
t
t
t
5\345
t
t
t
:1
:2
Display
000,
000,
001,20
002,31
003,44 40 1
004,45 0
005,25
006,31
007,44 40 2
008,40
009,44 40 3
6,370.52
0.00
68.5
890.50
60.11
950.61
72.9
1,312.20
88.57
1,400.77
85.
2,040.00
137.70
2,177.70
345.
1,725.00
116.44
1,841.44
5,967.70
402.82
Sets calculator to Program mode.
Clears program memory.
Stops program execution to
display AMOUNT.
Stops program execution to
display TAX.
Sets calculator to Run mode.
Clears registers R1 through R6.
First item.
AMOUNT for first item.
TAX for first item.
TOTAL for first item.
Second item.
AMOUNT for second item.
TAX for second item.
TOTAL for second item.
Third item.
AMOUNT for third item.
TAX for third item.
TOTAL for third item.
Fourth item.
AMOUNT for fourth item.
TAX for fourth item.
TOTAL for fourth item.
Sum of AMOUNT column.
Sum of TAX column.
100 Section 8: Programming Basics
Keystrokes
(RPN mode)
:3
Program execution is also automatically halted when the calculator overflows
(refer to page page 73) or attempts an improper operation that results in an Error
display. Either of these conditions signifies that the program itself probably
contains an error.
To determine at which program line execution has halted (in order to locate the
error), press any key to clear the Error display, then press fs to set the
calculator to Program mode and display that program line.
You may also want to display the current program line (by pressing fs) if
your program has halted at one of several t instructions in your program and
you want to determine which one that is. To continue executing the program
afterward:
1. Press fs to set the calculator back to Run mode.
2. If you want to resume execution from the program line at which execution
halted rather than from line 000, press gi followed by three digit
keys that specify the program line desired.
3. Press t to resume execution.
Stopping Program Execution Manually. Pressing any key while a program is
running halts program execution. You may want to do this if the calculated
results displayed by a running program appear to be incorrect (indicating that the
program itself is incorrect).
To halt program execution during a pause in a running program (that is, when
u is executed), press any key.
Display
6,370.52
Sum of TOTAL column.
After stopping program execution manually, you can determine at which
program line execution has halted and/or resume program execution as described
above.
Section 9
Branching and Looping
Although the instructions in a program normally are executed in order of their
program line numbers, in some situations it is desirable to have program
execution transfer or “branch” to a program line that is not the next line in
program memory. Branching also makes it possible to automatically execute
portions of a program more than once – a process called “looping.”
Simple Branching
The i (go to) instruction is used in a program to transfer execution to any
program line. The program line desired is specified by keying its three-digit line
number into the program line containing the i instruction. When the i
instruction is executed, program execution branches or “goes to” the program
line specified and then continues sequentially as usual.
001,002,003,004,005,006,007,008,
003causesprogramexecutionto
branchtoline003
You have already seen a common use of branching: the i000 instruction (that
is stored in program memory after the program you key in) transfers execution to
program line 000. A i instruction can be used to branch not only backward in
program memory – as in the case of i000 and as illustrated above – but also
forward in program memory. Backward branching is typically done to create
loops (as described next); forward branching is typically done in conjunction
with an o or m instruction for conditional branching (as described
afterward).
Looping
If a i instruction specifies a lower-numbered line in program memory, the
instructions in the program lines between the specified line and the i
instruction will be executed repeatedly. As can be seen in the illustration above
under Simple Branching, once the program begins executing the “loop” it will
execute it again and again.
101
102 Section 9: Branching and Looping
If you want to terminate the execution of a loop, you can include an o or m
instruction (described below) or an t instruction within the loop. You can
also terminate execution by pressing any key while the loop is being executed.
Example: The following program automatically amortizes the payments on a
home mortgage without requiring you to press f! for each payment. It will
amortize one month’s payments each time or one year’s payments each time the
loop is executed, depending on whether the number 1 or 12 is in the display
when you start running the program. Before running the program, we’ll
“initialize” it by storing the required data in the financial registers – just as we
would do if we were amortizing a single payment manually. We’ll run the
program for a $50,000 mortgage at 12¾% for 30 years, and we’ll key 1 into the
display just before running it in order to amortize monthly payments. For the
first two “passes” through the loop we’ll execute the program one line at a time,
using Ê, so that we can see the looping occurring; then we’ll use t to
execute the entire loop a third time before terminating execution.
KeystrokesDisplay
fs
fCLEARÎ
?0
:0
f!
gu
~
gu
000,
000,
001,44 0
002,45 0
003,42 11
004,43 31
005,34
006,43 31
Sets calculator to Program mode.
Clears program memory.
Stores the number from the
display into register R
. This
0
number will be the number of
payments to be amortized.
Recalls the number of payments
to be amortized. This program
line is the one to which program
execution will later branch. It is
included because after the first
time the loop is executed, the
number in the “display”
a
is
replaced by the result of !.
Amortizes payment(s).
Pauses to display amount of
payment(s) applied to interest.
Brings amount of payment(s)
applied to principal into
“display.”
a
Pauses to display amount of
payment(s) applied to principal.
Loading...
+ hidden pages
You need points to download manuals.
1 point = 1 manual.
You can buy points or you can get point for every manual you upload.