BA II PLUS
BA II PLUS™
Calculator
ii
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© 2005 Texas Instruments Incorporated
Contents
iii
Important Information................................................................... ii
USA FCC Information Concerning Radio Frequency Interferenceii
1 Overview of Calculator Operations..................................1
Turning On the Calculator ............................................................. 1
Turning Off the Calculator............................................................. 1
Selecting 2nd Functions ................................................................. 2
Reading the Display ....................................................................... 2
Setting Calculator Formats ........................................................... 4
Resetting the Calculator ................................................................ 6
Clearing Calculator Entries and Memories ................................... 6
Correcting Entry Errors................................................................... 7
Math Operations ............................................................................ 8
Memory Operations ..................................................................... 12
Calculations Using Constants....................................................... 13
Last Answer Feature..................................................................... 14
Using Worksheets: Tools for Financial Solutions ........................ 15
2 Time-Value-of-Money and Amortization Worksheets...21
TVM and Amortization Worksheet Variables............................. 22
Entering Cash Inflows and Outflows........................................... 25
Generating an Amortization Schedule ....................................... 25
Example: Computing Basic Loan Interest.................................... 26
Examples: Computing Basic Loan Payments ............................... 27
Examples: Computing Value in Savings ...................................... 28
Example: Computing Present Value in Annuities....................... 29
Example: Computing Perpetual Annuities.................................. 30
Example: Computing Present Value of Variable Cash Flows ..... 31
Example: Computing Present Value of a Lease With Residual
Value........................................................................................ 33
Example: Computing Other Monthly Payments......................... 34
Example: Saving With Monthly Deposits.................................... 35
Example: Computing Amount to Borrow and Down Payment. 36
Example: Computing Regular Deposits for a Specified Future
Amount ................................................................................... 37
Example: Computing Payments and Generating an Amortization
Schedule .................................................................................. 38
Example: Computing Payment, Interest, and Loan Balance After
a Specified Payment ............................................................... 39
3 Cash Flow Worksheet......................................................41
Cash Flow Worksheet Variables................................................... 41
iv
Uneven and Grouped Cash Flows................................................42
Entering Cash Flows......................................................................43
Deleting Cash Flows......................................................................43
Inserting Cash Flows .....................................................................44
Computing Cash Flows .................................................................44
Example: Solving for Unequal Cash Flows ..................................46
Example: Value of a Lease with Uneven Payments ....................48
4 Bond Worksheet ............................................................. 51
Bond Worksheet Variables...........................................................52
Bond Worksheet Terminology .....................................................54
Entering Bond Data and Computing Results ..............................54
Example: Computing Bond Price and Accrued Interest..............56
5 Depreciation Worksheet ................................................ 57
Depreciation Worksheet Variables ..............................................57
Entering Data and Computing Results........................................59
Example: Computing Straight-Line Depreciation.......................61
6 Statistics Worksheet ....................................................... 63
Statistics Worksheet Variables .....................................................63
Regression Models........................................................................65
Entering Statistical Data...............................................................66
Computing Statistical Results.......................................................67
7 Other Worksheets ........................................................... 69
Percent Change/Compound Interest Worksheet ........................69
Interest Conversion Worksheet....................................................72
Date Worksheet............................................................................74
Profit Margin Worksheet .............................................................76
Breakeven Worksheet ..................................................................78
Memory Worksheet......................................................................80
A Appendix — Reference Information.............................. 83
Formulas........................................................................................83
Error Messages..............................................................................94
Accuracy Information ...................................................................95
AOS™ (Algebraic Operating System) Calculations.....................96
Battery Information......................................................................97
In Case of Difficulty ......................................................................98
Texas Instruments Support and Service ....................................... 99
Texas Instruments (TI) Warranty Information ........................... 100
Index ............................................................................... 103
Overview of Calculator Operations 1
1
Overview of Calculator Operations
This chapter describes the basic operation of your BA II PLUS™
calculator, including how to:
• Turn on and turn off the calculator
• Select second functions
• Read the display and set calculator formats
• Clear the calculator and correct entry errors
• Perform math and memory operations
• Use the Last Answer feature
• Use worksheets
Turning On the Calculator
Turning Off the Calculator
Press $.
• The displayed value and any error condition clear.
• Any unfinished standard-calculator operation and worksheet
calculation in progress cancel.
Press $.
• If you turned off the calculator by pressing $, the
calculator returns to the standard-calculator mode
with a displayed value of zero.
All worksheets and formats for numbers, angle units,
dates, separators, and calculation method retain
previous values and configurations.
• If the Automatic Power Down™ (APD™) feature
turned off the calculator, the calculator turns on
exactly as you left it, saving display settings, stored
memory, pending operations, and error conditions.
2 Overview of Calculator Operations
• The Constant Memory™ feature retains all worksheet values and
settings, including the contents of the 10 memories and all format
settings.
Automatic Power Down™ (APD™) Feature
To prolong battery life, the Automatic Power Down (APD) feature turns
off the calculator automatically after about five minutes of inactivity.
The next time you press $, the calculator turns on exactly as you left
it, saving display settings and stored memory and any pending
operations or error conditions.
Selecting 2nd Functions
Reading the Display
The display shows the selected variable labels with values up to 10 digits.
(The calculator displays values exceeding 10 digits in scientific notation.)
The primary function of a key is printed on the key itself.
For example, the primary function of the $ key is to
turn on or turn off the calculator.
Most keys include a second function printed above the key.
To select a second function, press & and the
corresponding key. (When you press &, the 2nd indicator
appears in the upper left corner of the display.)
For example, pressing & U exits the selected
worksheet and returns the calculator to the standard-
calculator mode.
Note: To cancel after pressing &, press & again.
Overview of Calculator Operations 3
The indicators along the top of the display tell you which keys are active
and offer information about the status of the calculator.
Indicator Meaning
2nd Press a key to select its second function.
INV Press a key to select its inverse trigonometric function.
HYP Press a key to select its hyperbolic function.
COMPUTE Press % to compute a value for the displayed variable.
ENTER Press ! to assign the displayed value to the displayed
variable.
SET
Press & V to change the setting of the displayed
variable.
# $
Press " or # to display the previous or next variable in the
worksheet.
Note: To easily scroll up or down through a range of
variables, press and hold # or ".
DEL Press & W to delete a cash flow or statistical data point.
INS Press & X to insert a cash flow or statistical data point.
BGN TVM calculations use beginning-of-period payments. When
BGN is not displayed, TVM calculations use end-of-period
payments (END).
RAD Angle values appear in radians. When
RAD is not displayed,
angle values appear and must be entered in degrees.
The displayed value is entered in the selected worksheet.
The indicator clears following a computation.
The displayed value is computed in the selected worksheet.
When a value changes and invalidates a computed value,
the_indicator clears.
= The displayed variable is assigned the displayed value.
– The displayed value is negative.
4 Overview of Calculator Operations
Setting Calculator Formats
1. To access format options, press & |. The DEC indicator
appears with the selected number of decimal places.
2. To change the number of decimal places displayed, key in a value
and press !.
3. To access another calculator format, press # or " once for each
format.
For example, to access the angle unit format, press #. To access the
number-separator format, press "" "or # # #.
4. To change the selected format, press & V.
5. To change another calculator format, repeat step 3 and step 4.
— or —
To return to the standard-calculator mode, press & U.
— or —
To access a worksheet, press a worksheet key or key sequence.
Choosing the Number of Decimal Places Displayed
The calculator stores numeric values internally to an accuracy of 13 digits,
but you can specify the number of decimal places you want to display.
The calculator displays up to 10 digits with the floating-decimal option.
Results exceeding 10 digits appear in scientific notation.
You can change these calculator formats:
To Select Press Display Default
Number of
decimal
places
& | DEC 0–9 (Press 9 for
floating-decimal)
2
Angle units # DEG (degrees)
RAD (radians)
DEG
Dates # US (mm-dd-yyyy)
Eur (dd-mm-yyyy)
US
Number
separators
# US (1,000.00 )
Eur (1.000,00)
US
Calculation
method
# Chn (chain)
AOSé (algebraic
operating system)
Chn
Overview of Calculator Operations 5
Changing the number of decimal places affects the display only. Except
for amortization and depreciation results, the calculator does not round
internal values. To round the internal value, use the round function.
Note: All examples in this guidebook assume a setting of two decimal
places. Other settings might show different results.
Choosing the Angle Units
The angle unit value affects the display of results in trigonometric
calculations. When you select radians, the RAD indicator appears in the
upper right corner of the display. No indicator appears when you select
the default setting of degrees.
Using Dates
The calculator uses dates with the Bond and Date worksheets and the
French depreciation methods. To enter dates, use this convention:
mm.ddyy (US) or dd.mmyy (European). After you key in the date, press
!.
Choosing Calculation Methods
When you choose the chain (Chn) calculation method, the calculator
solves problems in the order that you enter them. (Most financial
calculators use Chn.)
For example, when you enter 3 H 2 < 4 N, the Chn answer is 20 (3 + 2 = 5,
5 * 4 = 20).
Using AOSé (algebraic operating system), the calculator solves problems
according to the standard rules of algebraic hierarchy, computing
multiplication and division operations before addition and subtraction
operations. (Most scientific calculators use AOS.)
For example, when you enter 3 H 2 < 4 N, the AOS answer is 11 (2 Q 4 =
8; 3 + 8 = 11).
Resetting Default Values
To reset default values for all of the calculator formats, press &
z with one of the formats displayed.
6 Overview of Calculator Operations
Resetting the Calculator
Because the calculator includes alternative methods that let you clear
data selectively, use reset carefully to avoid losing data needlessly. (See
“Clearing Calculator Entries and Memories
” on page 6.)
For example, you might reset the calculator before using it for the first
time, when starting a new calculation, or when having difficulty
operating the calculator and other possible solutions do not work. (See
“In Case of Difficulty
” on page 98.)
Pressing & } !
1. Press & }. The
RST ? and ENTER indicators appear.
Note: To cancel reset, press & U. 0.00 appears.
2. Press !. RST and 0.00 appear, confirming that the calculator is
reset.
Note: If an error condition exists, press P to clear the display before
attempting to reset.
Performing a Hard Reset
You can also reset the calculator by gently inserting a pointed object
(such as an unfolded paper clip or similar object) in the hole marked
RESET in back of the calculator.
Clearing Calculator Entries and Memories
Note: To clear variables selectively, see the specific worksheet chapters in
this guidebook.
Resetting the calculator:
• Clears the display, all 10 memories, any unfinished
calculations, and all worksheet data.
• Restores all default settings
• Returns operation to the standard-calculator mode
To clear Press
One character at a time, starting with the last digit
keyed in
*
An incorrect entry, error condition, or error
message
P
Overview of Calculator Operations 7
Correcting Entry Errors
Example: You mean to calculate 3 Q 1234.56 but instead enter 1234.86.
The prompted worksheet and reset default values & z
Calculator format settings and reset default values & |
& z
• Out of the prompted worksheet and return to
standard-calculator mode
• All pending operations in standard-calculator
mode
& U
• In a prompted worksheet, the variable value
keyed in but not entered (the previous value
appears)
• Any calculation started but not completed
P P
TVM worksheet variables and reset default values & U
& ^
One of the 10 memories (without affecting the
others)
Q D and a
memory number
key (0–9)
You can correct an entry without clearing a calculation, if
you make the correction before pressing an operation key
(for example, H or 4).
• To clear the last digit displayed, press *.
• To clear the entire number displayed, press P.
Note: Pressing P after you press an operation key clears
the calculation in progress.
To Press Display
Begin the expression. 3 <
3.00
Enter a number.
1234.86 1,234.86
Erase the entry error. * *
1,234.
Key in the correct number.
56 1,234.56
Compute the result. N
3,703.68
To clear Press
8 Overview of Calculator Operations
Math Operations
When you select the chain (Chn) calculation method, the calculator
evaluates mathematical expressions (for example, 3 + 2 Q 4) in the order
that you enter them.
Examples of Math Operations
These operations require you to press N to complete.
These operations do not require you to press N to complete.
To Press Display
Add 6 + 4
6 H 4 N
10.00
Subtract 6 N 4 6 B 4 N
2.00
Multiply 6 Q 4 6 < 4 N
24.00
Divide 6 P 4 6 6 4 N
1.50
Find universal power: 3
1.25
3 ; 1.25 N
3.95
Use parentheses: 7 Q (3 + 5) 7 < 9 3 H 5 : N
56.00
Find percent: 4% of $453 453 < 4 2 N
18.12
Find percent ratio: 14 to 25 14 6 25 2 N
56.00
Find price with percent add-on:
$498 + 7% sales tax
498 H 7 2
N
34.86
532.86
Find price with percent discount:
$69.99 N 10%
69.99 B 10 2
N
7.00
62.99
Find number of combinations where:
n = 52, r = 5
52 & s 5 N
2,598,960.00
Find number of permutations where:
n = 8, r = 3
8 & m 3 N
336.00
To Press Display
Square 6.3
2
6.3 4
39.69
Find square root:
15.5 3
3.94
Find reciprocal: 1/3.2 3.2 5
0.31
Find factorial: 5! 5 & g
120.00
Find natural logarithm: ln 203.45 203.45 >
5.32
15.5
Overview of Calculator Operations 9
* The random number you generate might be different.
** Angles can be computed in degrees or radians. Examples show
angles in degrees. (See “Choosing the Angle Units” on page 5.)
Universal Power ;
Press ; to raise the displayed positive number to any power (for
example, 2
-5
or 2
(1/3)
).
Note: Because the reciprocal of an even number (such as, 1/2, 1/4, 1/6) is
a complex number, you can only raise a negative number to an integer
power or the reciprocal of an odd number.
Find natural antilogarithm: e
.69315
.69315 & i
2.00
Round 2 P 3 to the set decimal format 2 6 3 N & o
0.67
Generate random number* & a
0.86
Store seed value D & a
0.86
Find sine:** sin(11.54°) 11.54 & d
0.20
Find cosine:** cos(120°) 120 & e
-0.50
Find tangent:** tan(76°) 76 & f
4.01
Find arcsine:** sin
-1
(.2)
.2 8 d
11.54
Find arccosine:** cos
-1
(-.5)
.5 S 8 e
120.00
Find arctangent:** tan
-1
(4)
4 8 f
75.96
Find hyperbolic sine: sinh(.5) .5 & c d
0.52
Find hyperbolic cosine: cosh(.5) .5 & c e
1.13
Find hyperbolic tangent: tanh(.5) .5 & c f
0.46
Find hyperbolic arcsine: sinh
-1
(5)
5 & c 8 d
2.31
Find hyperbolic arccosine: cosh
-1
(5)
5 & c 8 e
2.29
Find hyperbolic arctangent: tanh
-1
(.5)
.5 & c 8 f
0.55
To Press Display
10 Overview of Calculator Operations
Parentheses 9 :
Use parentheses to control the order in which the calculator evaluates a
numeric expression in division, multiplication, powers, roots, and
logarithm calculations. The calculator includes up to 15 levels of
parentheses and up to 8 pending operations.
Note: You do not have to press : for expressions ending in a series of
closed parentheses. Pressing N closes parentheses automatically,
evaluates the expression, and displays the final result. To view
intermediate results, press : once for each open parenthesis.
Factorial & g
The number for which you compute a factorial must be a positive integer
less than or equal to 69.
Random Numbers & a
The calculator generates a random real number between zero and one
(0<x<1) from a uniform distribution.
You can repeat a sequence of random numbers by storing a seed value in
the random number generator. Seed values help you recreate
experiments by generating the same series of random numbers.
To store a seed value, key in an integer greater than zero and press D
& a.
Combinations & s
The calculator computes the number of combinations of n items taken r
at a time. Both the n and r variables must be greater than or equal to 0.
Permutations & m
The calculator computes the number of permutations of n items taken r
at a time. Both the
n and r variables must be greater than or equal to 0.
Rounding & o
The calculator computes using the rounded, displayed form of a number
instead of the internally stored value.
Cr
n!
nr)! r!×–(
-----------------------------
=
Pr
n!
nr)!–(
------------------ -
=
Overview of Calculator Operations 11
For example, working in the Bond worksheet, you might want to round a
computed selling price to the nearest penny (two decimal places) before
continuing your calculation.
Note: The calculator stores values to an accuracy of up to 13 digits. The
decimal format setting rounds the displayed value but not the
unrounded, internally stored value. (See “Choosing the Number of
Decimal Places Displayed” on page 4.)
Scientific Notation ;
When you compute a value in the standard-decimal format that is either
too large or small to be displayed, the calculator displays it in scientific
notation, that is, a base value (or mantissa), followed by a blank space,
followed by an exponent.
With AOS™ selected, you can press ; to enter a number in scientific
notation. (See “Choosing Calculation Methods
” on page 5.)
For example, to enter 3 Q 10
3
, key in 3 < 10 ; 3.
12 Overview of Calculator Operations
Memory Operations
Clearing Memory
Clearing memory before you begin a new calculation is a critical step in
avoiding errors.
• To clear an individual memory, store a zero value in it.
• To clear all 10 calculator memories, press & { & z.
Storing to Memory
To store a displayed value to memory, press D and a numeric key (0–9).
• The displayed value replaces any previous value stored in the
memory.
• The Constant Memory feature retains all stored values when you
turn off the calculator.
Recalling From Memory
To recall a number stored in memory, press J and a numeric key (0–9).
Note: The recalled number remains in memory.
Memory Examples
Memory Arithmetic
Using memory arithmetic, you can perform a calculation with a stored
value and store the result with a single operation.
You can store values in any of 10 memories using the
standard calculator keys.
Note: You can also use the Memory worksheet. (See
“Memory Worksheet
” on page 80.)
• You can store in memory any numeric value within the
range of the calculator.
• To access a memory M0 through M9, press a numeric
key (0 through 9).
To Pr es s
Clear memory 4 (by storing a zero value in it)
0 D 4
Store 14.95 in memory 3 (M3) 14.95 D 3
Recall a value from memory 7 (M7) J 7
Overview of Calculator Operations 13
• Memory arithmetic changes only the value in the affected memory
and not the displayed value.
• Memory arithmetic does not complete any calculation in progress.
The table lists the available memory arithmetic functions. In each case,
the specified memory stores the result.
Calculations Using Constants
Example: Multiply 3, 7, and 45 by 8
To Pr es s
Add the displayed value to the value stored in memory 9
(
M9).
D H
9
Subtract the displayed value from the value stored in
memory 3 (M3).
D B 3
Multiply the value in memory 0 (M0) by the displayed value. D < 0
Divide the value in memory 5 (M5) by the displayed value. D 6 5
Raise the value in memory 4 (M4) to the power of the
displayed value.
D ; 4
To store a constant for use in repetitive calculations, enter
a number and an operation, and then press &`.
To use the stored constant, key in a value and press N.
Note: Pressing a key other than a number or N clears the
constant.
To Press Display
Clear the calculator. & U 0.00
Enter the value for the first calculation.
3
3
Enter the operation and a constant value. <
8 8
Store the operation and value, and then
calculate.
& ` N 24.00
Calculate 7
Q 8.
7 N 56.00
Compute 45
Q 8.
45 N 360.00
14 Overview of Calculator Operations
Keystrokes for Constant Calculations
This table shows how to create a constant for various operations.
*The letter c denotes the constant value.
**Repeat constant calculations with n N.
Last Answer Feature
To display the last answer computed, press &x.
Note: The calculator changes the value of the last answer whenever it
calculates a value automatically or whenever you:
• Press ! to enter a value.
• Press % to compute a value.
• Press N to complete a calculation.
Example: Using the Last Answer in a Calculation
To* Press**
Add c to each subsequent entry n H & ` c N
Subtract c from each subsequent entry n B & ` c N
Multiply each subsequent entry by cn < & ` c N
Divide each subsequent entry by cn 6 & ` c N
Raise each subsequent entry to the power of cn ; & ` c N
Add c% of each subsequent entry to that entry n H & ` c 2 N
Subtract c% of each subsequent entry from the
entry
n B & ` c 2 N
Use the Last Answer (
ANS) feature with problems that call
repeatedly for the same value or to copy a value:
• From one place to another within the same worksheet
• From one worksheet to another
• From a worksheet to the standard-calculator mode
• From the standard-calculator mode to a worksheet
To Press Display
Key in and complete a calculation 3 H 1 N 4.00
Overview of Calculator Operations 15
Using Worksheets: Tools for Financial Solutions
Each worksheet is independent of the others: operations in a worksheet
do not affect variables in other worksheets. When you exit a worksheet
or turn off the calculator, the calculator retains all worksheet data.
Key in a new calculation 2 ; 2.00
Recall the last answer & x 4.00
Complete the calculation N 16.00
The calculator contains worksheets with embedded
formulas to solve specific problems. You apply settings or
assign known values to worksheet variables and then
compute the unknown value. Changing the values lets you
ask what if questions and compare results.
Except for TVM variables, accessed in the standard-
calculator mode, all variables are prompted.
For example, to assign values to amortization variables, you
must first press & \ to access the Amortization
worksheet.
To select Function Press
TVM worksheet
(Chapter 2)
Analyzes equal cash flows, for
example, annuities, loans,
mortgages, leases, and savings
,, -, .,
/, 0, or
& [
Amortization worksheet
(Chapter 2)
Performs amortization
calculations and generates an
amortization schedule
& \
Cash Flow worksheet
(Chapter 3)
Analyzes unequal cash flows by
calculating net present value
and internal rate of return
& '
Bond worksheet
(Chapter 4)
Computes bond price and yield
to maturity or call
& l
Depreciation worksheet
(Chapter 5)
Generates a depreciation
schedule using one of six
depreciation methods
& p
To Press Display
16 Overview of Calculator Operations
Accessing the TVM Worksheet Variables
Statistics worksheet
(Chapter 6)
Analyzes statistics on one- or
two-variable data using four
regression analysis options
& k
Percent
Change/Compound
Interest worksheet
(Chapter 7)
Computes percent change,
compound interest, and cost-
sell markup
& q
Interest Conversion
worksheet
(Chapter 7)
Converts interest rates
between nominal rate (or
annual percentage rate) and
annual effective rate
& v
Date worksheet
(Chapter 7)
Computes number of days
between two dates, or
date/day of the week a
specified number of days is
from a given date
& u
Profit Margin worksheet
(Chapter 7)
Computes cost, selling price,
and profit margin
& w
Breakeven worksheet
(Chapter 7)
Analyzes relationship between
fixed cost, variable cost, price,
profit, and quantity
& r
Memory worksheet
(Chapter 7)
Accesses storage area for up to
10 values
& {
• To assign values to the TVM worksheet variables, use
the five TVM keys (,, -, ., /, 0).
• To access other TVM worksheet functions, press the &
key, and then press a TVM function key (
xP/Y, P/Y,
BGN). (See “TVM and Amortization Worksheet
Variables” on page 22.)
Note: You can assign values to TVM variables while in a
prompted worksheet, but you must return to the
standard-calculator mode to calculate TVM values or
clear the TVM worksheet.
To select Function Press
Overview of Calculator Operations 17
Accessing Prompted-Worksheet Variables
After you access a worksheet, press # or " to select variables. For
example, press & \ to access the Amortization worksheet, and
then press # or " to select the amortization variables (
P1, P2, BAL, PRN,
INT
).(See “TVM and Amortization Worksheet Variables” on page 22.)
Indicators prompt you to select settings, enter values, or compute results.
For example, the i#
$ indicators remind you to press # or " to select
other variables. (See “Reading the Display” on page 2.)
To return to the standard-calculator mode, press & U.
Types of Worksheet Variables
• Enter-only
• Compute-only
• Automatic-compute
• Enter-or-compute
•Settings
Note: The = sign displayed between the variable label and value
indicates that the variable is assigned the value.
Enter-Only Variables
Values for enter-only variables must be entered, cannot be computed,
and are often limited to a specified range, for example,
P/Y and C/Y. The
value for an enter-only variable can be:
• Entered directly from the keyboard.
• The result of a math calculation.
• Recalled from memory.
• Obtained from another worksheet using the last answer feature.
When you access an enter-only variable, the calculator displays the
variable label and ENTER indicator. The ENTER indicator reminds you to
press ! after keying in a value to assign the value to the variable.
After you press !, the indicator confirms that the value is assigned.
Compute-Only Variables
You cannot enter values manually for compute-only variables, for
example, net present value (
NPV). To compute a value, display a
compute-only variable and press %. The calculator computes and
displays the value based on the values of other variables.
18 Overview of Calculator Operations
When you display a compute-only variable, the COMPUTE indicator
reminds you to press % to compute its value. After you press %, the
indicator confirms that the displayed value has been computed.
Automatic-Compute Variables
When you press # or " to display an automatic-compute variable (for
example, the Amortization worksheet
INT variable), the calculator
computes and displays the value automatically without you having to
press %.
Enter-or-Compute Variables in the TVM Worksheet
You can either enter or compute values for the TVM worksheet variables
(N, I/Y, PV, PMT, and FV).
Note: Although you do not have to be in the standard-calculator mode
to assign values to these variables, you must be in the standard-calculator
mode to compute their values.
• To assign the value of a TVM variable, key in a number and press a
variable key.
• To compute the value of a TVM variable, press %, and then press the
variable key. The calculator computes and displays the value based
on the values of other variables.
Enter-or-Compute Variables in Prompted Worksheets
You can either enter or compute values for some prompted worksheet
variables (for example, the Bond worksheet YLD and PRI variables).
When you select an enter-or-compute variable, the calculator displays
the variable label with the
ENTER and COMPUTE indicators.
•The
ENTER indicator prompts you to press ! to assign the keyed-
in value to the displayed variable.
•The COMPUTE indicator prompts you to press % to compute a
value for the variable.
Selecting Worksheet Settings
Many prompted worksheets contain variables consisting of two or more
options, or settings (for example, the Date worksheet ACT/360 variable).
When you select variables with settings, the calculator displays the
SET
indicator and the current setting.
To scroll through the settings of a variable, press & V once for each
setting.
Overview of Calculator Operations 19
Display Indicators
•The indicator confirms that the calculator entered the displayed
value in the worksheet.
•The indicator confirms that the calculator computed the displayed
value.
• When a change to the worksheet invalidates either entered or
computed values, the and indicators disappear.
20 Overview of Calculator Operations
Time-Value-of-Money and Amortization Worksheets 21
2
Time-Value-of-Money and Amortization
Worksheets
After solving a TVM problem, you can use the Amortization worksheet to
generate an amortization schedule.
• To access a TVM variable, press a TVM key (,, -, ., /, or 0).
• To access the prompted Amortization worksheet, press & \.
Use the Time-Value-of-Money (TVM) variables to solve
problems with equal and regular cash flows that are either
all inflows or all outflows (for example, annuities, loans,
mortgages, leases, and savings).
For cash-flow problems with unequal cash flows, use the
Cash Flow worksheet. (See “Cash Flow Worksheet
” on
page 41.)
22 Time-Value-of-Money and Amortization Worksheets
TVM and Amortization Worksheet Variables
Note: This guidebook categorizes calculator variables by the method of
entry. (See “Types of Worksheet Variables” on page 17.)
Using the TVM and Amortization Variables
Because the calculator stores values assigned to the TVM variables until
you clear or change them, you should not have to perform all steps each
time you work a problem.
• To assign a value to a TVM variable, key in a number and press a TVM
key (,, -, ., /, 0).
• To change the number of payments (
P/Y), press &[, key in a
number, and press !. To change the compounding periods (C/Y),
press &[ #, key in a number, and press !.
• To change the payment period (END/BGN), press & ], and then
press & V.
• To compute a value for the unknown variable, press %, and then
press the key for the unknown variable.
Variable Key Display Type of Variable
Number of periods ,
N
Enter-or-compute
Interest rate per year -
I/Y
Enter-or-compute
Present value .
PV
Enter-or-compute
Payment /
PMT
Enter-or-compute
Future value 0
FV
Enter-or-compute
Number of payments per year & [
P/Y
Enter-only
Number of compounding
periods per year
#
C/Y
Enter-only
End-of-period payments & ]
END
Setting
Beginning-of-period
payments
& V
BGN
Setting
Starting payment & \
P1
Enter-only
Ending payment #
P2
Enter-only
Balance #
BAL
Auto-compute
Principal paid #
PRN
Auto-compute
Interest paid #
INT
Auto-compute
Time-Value-of-Money and Amortization Worksheets 23
• To generate an amortization schedule, press & \, enter the
first and last payment number in the range (
P1 and P2), and press "
or # to compute values for each variable (BAL, PRN, and INT).
Resetting the TVM and Amortization Worksheet Variables
• To reset all calculator variables and formats to default values
(including TVM and amortization variables), press & } !:
• To reset only the TVM variables (
N, I/Y, PV, PMT, FV) to default values,
press & ^.
• To reset P/Y and C/Y to default values, press & [ & z.
• To reset the Amortization worksheet variables (P1, P2, BAL, PRN,
INT) to default values, press & z while in the Amortization
worksheet.
• To reset END/BGN to the default value, press & ] & z.
Clearing the Unused Variable
For problems using only four of the five TVM variables, enter a value of
zero for the unused variable.
For example, to determine the present value (
PV) of a known future
value (FV) with a known interest rate (I/Y) and no payments, enter 0 and
press
PMT.
Entering Positive and Negative Values for Outflows and
Inflows
Enter negative values for outflows (cash paid out) and positive values for
inflows (cash received).
Note: To enter a negative value, press S after entering the number. To
change a negative value to positive, press S.
Variable Default Variable Default
N
0
END/BGN END
I/Y
0
P1
1
PV
0
P2
1
PMT
0
BAL
0
FV
0
PRN
0
P/Y
1
INT
0
C/Y
1
24 Time-Value-of-Money and Amortization Worksheets
Entering Values for I/Y, P/Y, and C/Y
•Enter I/Y as the nominal interest rate. The TVM worksheet
automatically converts
I/Y to a per period rate based on the values of
P/Y and C/Y.
• Entering a value for P/Y automatically enters the same value for C/Y.
(You can change C/Y.)
Specifying Payments Due With Annuities
Use END/BGN to specify whether the transaction is an ordinary annuity
or an annuity due.
•Set
END for ordinary annuities, in which payments occur at the end
of each payment period. (This category includes most loans.)
•Set BGN for annuities due, in which payments occur at the beginning
of each payment period. (This category includes most leases.)
Note: When you select beginning-of-period payments, the BGN indicator
appears. (No indicator appears for END payments.)
Updating P1 and P2
To update P1 and P2 for a next range of payments, press % with P1 or
P2 displayed.
Different Values for BAL and FV
The computed value for BAL following a specified number of payments
might be different than the computed value for FV following the same
number of payments.
• When solving for
BAL, PRN, and INT, the calculator uses the PMT
value rounded to the number of decimal places specified by the
decimal format.
• When solving for FV, the calculator uses the unrounded value for
PMT.
Entering, Recalling, and Computing TVM Values
• To enter a TVM value, key in the value and store it by pressing a TVM
key (,, -, ., /, 0).
• To display a stored TVM value, press J and a TVM key.
You can enter or recall a value for any of the five TVM variables (
N, I/Y,
PV, PMT, or FV) in either the standard calculator mode or a worksheet
mode. The information displayed depends on which mode is selected.
• In standard calculator mode, the calculator displays the variable
label, the = sign, and the value entered or recalled.
Time-Value-of-Money and Amortization Worksheets 25
• In worksheet modes the calculator displays only the value you enter
or recall, although any variable label previously displayed remains
displayed.
Note: You can tell that the displayed value is not assigned to the
displayed variable, because the = indicator is not displayed.
To compute a TVM value, press % and a TVM key in standard-calculator
mode.
Using [xP/Y] to Calculate a Value for N
1. Key in the number of years, and then press & Z to multiply by
the stored
P/Y value. The total number of payments appears.
2. To assign the displayed value to
N for a TVM calculation, press ,.
Entering Cash Inflows and Outflows
The calculator treats cash received (inflows) as a positive value and cash
invested (outflows) as a negative value.
• You must enter cash inflows as positive values and cash outflows as
negative values.
• The calculator displays computed inflows as positive values and
computed outflows as negative values.
Generating an Amortization Schedule
The Amortization worksheet uses TVM values to compute an
amortization schedule either manually or automatically.
Generating an Amortization Schedule Manually
1. Press & \. The current P1 value appears.
2. To specify the first in a range of payments, key in a value for P1 and
press !.
3. Press #. The current P2 value appears.
4. To specify the last payment in the range, key in a value for P2 and
press !.
5. Press # to display each of the automatically computed values:
•
BAL— the remaining balance after payment P2
• PRN— the principal
• INT— the interest paid over the specified range
26 Time-Value-of-Money and Amortization Worksheets
6. Press & \.
— or —
If
INT is displayed, press # to display P1 again.
7. To generate the amortization schedule, repeat steps 2 through 5 for
each range of payments.
Generating an Amortization Schedule Automatically
After entering the initial values for P1 and P2, you can compute an
amortization schedule automatically.
1. Press & \.
— or —
If
INT is displayed, press # to display the current P1 value.
2. Press %. Both
P1 and P2 update automatically to represent the
next range of payments.
The calculator computes the next range of payments using the same
number of periods used with the previous range of payments. For
example, if the previous range was 1 through 12 (12 payments),
pressing % updates the range to 13 through 24 (12 payments).
3. Press # to display
P2.
• If you press % with P1 displayed, a new value for P2 will be
displayed automatically. (You can still enter a new value for P2.)
• If you did not press % with P1 displayed, you can press %
with P2 displayed to enter values for both P1 and P2 in the next
range of payments.
4. Press # to display each of the automatically computed values for
BAL, PRN, and INT in the next range of payments.
5. Repeat steps 1 through 4 until the schedule is complete.
Example: Computing Basic Loan Interest
If you make a monthly payment of $425.84 on a 30-year mortgage for
$75,000, what is the interest rate on your mortgage?
To Press Display
Set payments per year to 12. & [
12 !
P/Y=
12.00
Return to standard-calculator
mode.
& U
0.00
Enter number of payments
using the payment multiplier.
30 & Z ,
N=
360.00
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