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HP 12C Platinum Owner ’ s Handbook and Problem-Solving Guide

HP 12C Platinum
Owner’s Handbook
and
Problem-Solving Guide
© Copyright 2003 Hewlett-Packard Development Company, L.P.
Introduction
About This Handbook
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
Introduction 3
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.
Contents
Introduction ...................................................................................... 2
About This Handbook ..................................................................................... 2
Financial Calculations in the United Kingdom ................................................ 3
For More Solutions to Financial Problems...................................................... 3
Part I: Problem Solving................................................15
Section 1: Getting Started................................................................... 16
Power On and Off......................................................................................... 16
Low-Power Indication ............................................................................. 16
The Keyboard ............................................................................................... 16
Keying in Numbers ................................................................................. 17
Digit Separators...................................................................................... 17
Negative Numbers.................................................................................. 17
Keying in Large Numbers....................................................................... 18
The CLEAR Keys ................................................................................... 18
The RPN and ALG Keys......................................................................... 19
Simple Arithmetic Calculations in RPN Mode............................................... 19
Chain Calculations in RPN Mode ................................................................. 20
Storage Registers......................................................................................... 23
Storing and Recalling Numbers.............................................................. 24
Clearing Storage Registers .................................................................... 25
Storage Register Arithmetic.................................................................... 25
Section 2: Percentage and Calendar Functions............................ 27
Percentage Functions................................................................................... 27
Percentages ........................................................................................... 27
Net amount............................................................................................. 27
Percent Difference.................................................................................. 28
Percent of Total ...................................................................................... 29
Calendar Functions ...................................................................................... 30
Date Format............................................................................................ 30
Future or Past Dates .............................................................................. 31
Number of Days Between Dates ............................................................ 32
Section 3: Basic Financial Functions............................................... 34
The Financial Registers................................................................................ 34
Storing Numbers Into the Financial Registers........................................ 34
Displaying Numbers in the Financial Registers...................................... 34
Clearing the Financial Registers............................................................. 34
Simple Interest Calculations ......................................................................... 35
Financial Calculations and the Cash Flow Diagram ..................................... 36
The Cash Flow Sign Convention ............................................................ 38
The Payment Mode ................................................................................ 38
Generalized Cash Flow Diagrams.......................................................... 39
5
6 Contents
Compound Interest Calculations .................................................................. 41
Specifying the Number of Compounding Periods and the Periodic
Interest Rate ........................................................................................... 41
Calculating the Number of Payments or Compounding Periods ............ 41
Calculating the Periodic and Annual Interest Rates............................... 45
Calculating the Present Value ................................................................ 46
Calculating the Payment Amount ........................................................... 48
Calculating the Future Value .................................................................. 49
Odd-Period Calculations......................................................................... 51
Amortization.................................................................................................. 54
Section 4: Additional Financial Functions ...................................... 58
Discounted Cash Flow Analysis: NPV and IRR............................................ 58
Calculating Net Present Value (NPV)..................................................... 59
Calculating Internal Rate of Return (IRR)............................................... 63
Reviewing Cash Flow Entries................................................................. 64
Changing Cash Flow Entries .................................................................. 66
Bond Calculations......................................................................................... 67
Bond Price.............................................................................................. 67
Bond Yield .............................................................................................. 68
Depreciation Calculations............................................................................. 68
Section 5: Additional Operating Features....................................... 70
Continuous Memory ..................................................................................... 70
The Display................................................................................................... 70
Status Indicators..................................................................................... 70
Number Display Formats........................................................................ 71
Scientific Notation Display Format.......................................................... 72
Special Displays ..................................................................................... 73
The
~ Key................................................................................................ 74
The
F Key ............................................................................................... 74
Arithmetic Calculations With Constants.................................................. 75
Recovering From Errors in Digit Entry.................................................... 75
Section 6: Statistics Functions .......................................................... 76
Accumulating Statistics................................................................................. 76
Correcting Accumulated Statistics................................................................ 77
Mean............................................................................................................. 77
Standard Deviation ....................................................................................... 78
Linear Estimation.......................................................................................... 79
Weighted Mean ............................................................................................ 81
Section 7: Mathematics and Number-Alteration Functions ....... 82
One-Number Functions ................................................................................ 82
The Power Function ..................................................................................... 84
Contents 7
Part II: Programming....................................................85
Section 8: Programming Basics........................................................ 86
Why Use Programs? .................................................................................... 86
Creating a Program ...................................................................................... 86
Running a Program ...................................................................................... 87
Program Memory.......................................................................................... 88
Identifying Instructions in Program Lines................................................ 89
Displaying Program Lines....................................................................... 90
The
i000 Instruction and Program Line 000..................................... 91
Expanding Program Memory.................................................................. 91
Setting the Calculator to a Particular Program Line ............................... 93
Executing a Program One Line at a Time .................................................... 94
Interrupting Program Execution.................................................................... 95
Pausing During Program Execution ....................................................... 95
Stopping Program Execution .................................................................. 98
Section 9: Branching and Looping................................................. 101
Simple Branching ....................................................................................... 101
Looping....................................................................................................... 101
Conditional Branching ................................................................................ 104
Section 10: Program Editing............................................................. 110
Changing the Instruction in a Program Line............................................... 110
Adding Instructions at the End of a Program.............................................. 111
Adding Instructions Within a Program ........................................................ 112
Adding Instructions by Replacement.................................................... 112
Adding Instructions by Branching ......................................................... 113
Section 11: Multiple Programs......................................................... 117
Storing Another Program............................................................................ 117
Running Another Program.......................................................................... 119
Part III: Solutions........................................................121
Section 12: Real Estate and Lending ............................................. 122
Annual Percentage Rate Calculations With Fees....................................... 122
Price of a Mortgage Traded at a Discount or Premium .............................. 124
Yield of a Mortgage Traded at a Discount or Premium .............................. 125
The Rent or Buy Decision........................................................................... 127
Deferred Annuities...................................................................................... 131
Section 13: Investment Analysis..................................................... 134
Partial-Year Depreciation ........................................................................... 134
Straight-Line Depreciation .................................................................... 134
Declining-Balance Depreciation ........................................................... 137
Sum-of-the-Years-Digits Depreciation.................................................. 139
Full- and Partial-Year Depreciation with Crossover.................................... 141
Excess Depreciation................................................................................... 145
Modified Internal Rate of Return................................................................. 145
8 Contents
Section 14: Leasing............................................................................ 148
Advance Payments..................................................................................... 148
Solving For Payment ............................................................................ 148
Solving for Yield.................................................................................... 150
Advance Payments With Residual ............................................................. 152
Solving for Payment ............................................................................. 152
Solving For Yield .................................................................................. 154
Section 15: Savings............................................................................ 156
Nominal Rate Converted to Effective Rate................................................. 156
Effective Rate Converted to Nominal Rate................................................. 157
Nominal Rate Converted to Continuous Effective Rate.............................. 158
Section 16: Bonds............................................................................... 159
30/360 Day Basis Bonds ............................................................................ 159
Annual Coupon Bonds................................................................................ 161
Appendixes ................................................................ 165
Appendix A: RPN and the Stack .................................................... 166
Getting Numbers Into the Stack: The \ Key ......................................... 167
Termination of Digit Entry ..................................................................... 168
Stack Lift............................................................................................... 168
Rearranging Numbers in the Stack ............................................................ 168
The
~ Key........................................................................................ 168
The
d Key.......................................................................................... 168
One-Number Functions and the Stack ....................................................... 169
Two-Number Functions and the Stack ....................................................... 169
Mathematics Functions......................................................................... 169
Percentage Functions........................................................................... 170
Calendar and Financial Functions.............................................................. 171
The LAST X Register and the
Chain Calculations in RPN Mode ............................................................... 172
Arithmetic Calculations with Constants ...................................................... 173
Appendix B: Algebraic Mode (ALG) .............................................. 175
Simple Arithmetic calculations in ALG mode.............................................. 175
Keying in Negative Numbers (
Chain Calculations in ALG mode................................................................ 176
Percentage Functions................................................................................. 176
Percent Difference................................................................................ 177
Percent of Total .................................................................................... 177
The Power Function ................................................................................... 178
Appendix C: More About L ......................................................... 179
Appendix D: Error Conditions ........................................................ 181
Error 0: Mathematics .................................................................................. 181
Error 1: Storage Register Overflow ............................................................ 181
Error 2: Statistics ........................................................................................ 182
Error 3: IRR ................................................................................................ 182
F KEY ................................................... 172
Þ)........................................................... 175
Contents 9
Error 4: Memory.......................................................................................... 182
Error 5: Compound Interest........................................................................ 182
Error 6: Storage Registers.......................................................................... 183
Error 7: IRR ................................................................................................ 183
Error 8: Calendar........................................................................................ 184
Error 9: Service........................................................................................... 184
Pr Error ....................................................................................................... 184
Appendix E: Formulas Used ............................................................ 185
Percentage ................................................................................................. 185
Interest........................................................................................................ 185
Simple Interest...................................................................................... 185
Compound Interest ............................................................................... 185
Amortization................................................................................................ 186
Discounted Cash Flow Analysis ................................................................. 187
Net Present Value ................................................................................ 187
Internal Rate of Return ......................................................................... 187
Calendar..................................................................................................... 187
Actual Day Basis .................................................................................. 187
30/360 Day Basis ................................................................................. 188
Bonds ......................................................................................................... 188
Depreciation ............................................................................................... 189
Straight-Line Depreciation .................................................................... 189
Sum-of-the-Years-Digits Depreciation.................................................. 190
Declining-Balance Depreciation ........................................................... 190
Modified Internal Rate of Return................................................................. 190
Advance Payments..................................................................................... 191
Interest Rate Conversions .......................................................................... 191
Finite Compounding ............................................................................. 191
Continuous Compounding.................................................................... 191
Statistics ..................................................................................................... 191
Mean..................................................................................................... 191
Weighted Mean .................................................................................... 192
Linear Estimation.................................................................................. 192
Standard Deviation............................................................................... 192
Factorial................................................................................................ 192
The Rent or Buy Decision........................................................................... 193
Appendix F: Battery, Warranty, and Service Information ........ 195
Battery ........................................................................................................ 195
Low-Power Indication ................................................................................. 195
Installing a New Battery........................................................................ 195
Verifying Proper Operation (Self-Tests) ..................................................... 196
Warranty ..................................................................................................... 198
Service........................................................................................................ 200
Potential For Radio/Television Interference (for U.S.A. Only) .................... 201
Temperature Specifications........................................................................ 201
Noise Declaration ....................................................................................... 201
Regulation applying to The Netherlands .................................................... 202
10 Contents
Appendix G: United Kingdom Calculations ................................ 203
Mortgages................................................................................................... 203
Annual Percentage Rate (APR) Calculations............................................. 203
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.
Keystrokes Display
fCLEARHf2
4gA
6gC
500P
g× $
a Don’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 Easy 13
6% annually, compounded monthly. What payment amount would be required in order to accumulate $10,925.75 in the 14 years remaining?
Keystrokes Display
fCLEARG
14gA
6gC
10925.76M
g 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.
Keystrokes Display
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 Started 17
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:
Keystrokes Display
1.7814Æ12
Numbers entered in scientific notation can be used in calculations just like any other number.
1.7814 12
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:
O Display and X-register. fCLEAR² Statistics registers (R
registers, and display.
fCLEARÎ Program memory (only when pressed in
Program mode).
fCLEARG Financial registers. fCLEARH Data storage registers, financial registers,
stack and LAST X registers, and display.
through R6), stack
1
Section 1: Getting Started 19
The RPN and ALG Keys
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 mode ALG 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 Started 21
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!):
Youdoone operation at a time ...
... and you see the results of each operation immediately.
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 Started 23
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 Started 25
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:
number formerly
in register
Storage register arithmetic is possible with only registers R
number in display
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
Keystrokes Display
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?
Keystrokes Display
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 Functions 29
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:
Keystrokes Display
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 Functions 31
For example, to key in April 7, 2004:
Keystrokes Display
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
Keystrokes Display
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.
Keystrokes Display
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.
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