Texas Instruments Calculator User Manual
BA II PLUS™
PROFESSIONAL
Calculator
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This equipment has been tested and found to comply with the limits for a
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© 2004 Texas Instruments Incorporated
ii
Table of Contents
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
....................................................................................................... 19
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
Uneven and Grouped Cash Flows................................................ 43
Entering Cash Flows ..................................................................... 43
Table of Contents iii
Deleting Cash Flows......................................................................44
Inserting Cash Flows .....................................................................44
Computing Cash Flows .................................................................45
Example: Solving for Unequal Cash Flows .................................47
Example: Value of a Lease with Uneven Payments ....................49
4 Bond Worksheet ............................................................. 53
Bond Worksheet Variables ...........................................................54
Bond Worksheet Terminology .....................................................56
Entering Bond Data and Computing Results ..............................56
Example: Computing Bond Price, Accrued Interest, and
Modified Duration..................................................................58
5 Depreciation Worksheet ................................................ 59
Depreciation Worksheet Variables ..............................................59
Entering Data and Computing Results........................................61
Example: Computing Straight-Line Depreciation.......................62
6 Statistics Worksheet ....................................................... 65
Statistics Worksheet Variables ..................................................... 65
Regression Models........................................................................67
Entering Statistical Data...............................................................68
Computing Statistical Results.......................................................69
7 Other Worksheets ........................................................... 71
Percent Change/Compound Interest Worksheet ........................71
Interest Conversion Worksheet....................................................74
Date Worksheet............................................................................76
Profit Margin Worksheet .............................................................78
Breakeven Worksheet ..................................................................80
Memory Worksheet......................................................................82
....................................................................................................... 83
A Appendix — Reference Information.............................. 85
Formulas........................................................................................85
Error Messages..............................................................................96
Accuracy Information ...................................................................98
AOS™ (Algebraic Operating System) Calculations.....................98
Battery Information......................................................................99
In Case of Difficulty ....................................................................100
Texas Instruments Support and Service .....................................101
Texas Instruments (TI) Warranty Information ...........................102
Index.............................................................................. 105
iv Table of Contents
Overview of Calculator Operations
This chapter describes the basic operation of your BA II PLUS™
PROFESSIONAL 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
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.
1
Turning Off the Calculator
Press $.
• The displayed value and any error condition clear.
• Any unfinished standard-calculator operation and worksheet
calculation in progress cancel.
Overview of Calculator Operations 1
• 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
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 standardcalculator mode.
Note: To cancel after pressing &, press & again.
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.)
2 Overview of Calculator Operations
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
# $
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
RAD Angle values appear in radians. When
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 ".
BGN is not displayed, TVM calculations use end-of-period
payments (END).
RAD is not displayed,
angle values appear and must be entered in degrees.
= The displayed variable is assigned the displayed value.
– The displayed value is negative.
Overview of Calculator Operations 3
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.
Setting Calculator Formats
You can change these calculator formats:
To Select Press Display Default
Number of
decimal
& |
DEC 0–9 (Press 9 for
floating-decimal)
places
Angle units # DEG (degrees)
RAD (radians)
Dates # US (mm-dd-yyyy)
Eur (dd-mm-yyyy)
Number
separators
Calculation
method
# US (1,000.00 )
Eur (1.000,00)
# Chn (chain)
AOSé (algebraic
operating system)
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.
2
DEG
US
US
Chn
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.
4 Overview of Calculator Operations
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. (See
“Rounding & o” on page 10.)
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.
Overview of Calculator Operations 5
Resetting the Calculator
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
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 100.)
Pressing & } !
1. Press & }. The
Note: To cancel reset, press & U.
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.
RST ? and ENTER indicators appear.
0.00 appears.
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.
To clear Press
One character at a time, starting with the last digit
keyed in
An incorrect entry, error condition, or error
message
6 Overview of Calculator Operations
*
P
To clear Press
The prompted worksheet and reset default values & z
Calculator format settings and reset default values & |
& z
• Out of the prompted worksheet and return to
& U
standard-calculator mode
• All pending operations in standard-calculator
mode
• In a prompted worksheet, the variable value
P P
keyed in but not entered (the previous value
appears)
• Any calculation started but not completed
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)
Correcting Entry Errors
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.
Example: You mean to calculate 3 Q 1234.56 but instead enter 1234.86.
To Press Display
Begin the expression.
Enter a number.
3 <
1234.86 1,234.86
Erase the entry error. * *
Key in the correct number.
56 1,234.56
Compute the result. N
Overview of Calculator Operations 7
3.00
1,234.
3,703.68
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.
To Press Display
Add 6 + 4 6 H 4 N
Subtract 6 N 4 6 B 4 N
Multiply 6 Q 4 6 < 4 N
Divide 6 P 4 6 6 4 N
Find universal power: 3
1.25
3 ; 1.25 N
Use parentheses: 7 Q (3 + 5) 7 < 9 3 H 5 : N
Find percent: 4% of $453 453 < 4 2 N
Find percent ratio: 14 to 25 14 6 25 2 N
Find price with percent add-on:
$498 + 7% sales tax
Find price with percent discount:
$69.99 N 10%
Find number of combinations where:
498 H 7 2
N
69.99 B 10 2
N
52 & s 5 N
n = 52, r = 5
Find number of permutations where:
8 & m 3 N
n = 8, r = 3
2,598,960.00
10.00
2.00
24.00
1.50
3.95
56.00
18.12
56.00
34.86
532.86
7.00
62.99
336.00
These operations do not require you to press N to complete.
To Press Display
Square 6.3
2
Find square root:
15.5
6.3 4
15.5 3
Find reciprocal: 1/3.2 3.2 5
Find factorial: 5! 5 & g
Find natural logarithm: ln 203.45 203.45 >
8 Overview of Calculator Operations
39.69
3.94
0.31
120.00
5.32
To Press Display
Find natural antilogarithm: e
.69315
.69315 & i
Round 2 P 3 to the set decimal format 2 6 3 N & o
Generate random number* & a
Store seed value D & a
Find sine:** sin(11.54°) 11.54 & d
Find cosine:** cos(120°) 120 & e
Find tangent:** tan(76°) 76 & f
Find arcsine:** sin-1(.2)
Find arccosine:** cos-1(-.5)
Find arctangent:** tan-1(4)
.2 8 d
.5 S 8 e
4 8 f
Find hyperbolic sine: sinh(.5) .5 & c d
Find hyperbolic cosine: cosh(.5) .5 & c e
Find hyperbolic tangent: tanh(.5) .5 & c f
Find hyperbolic arcsine: sinh-1(5)
Find hyperbolic arccosine: cosh-1(5)
Find hyperbolic arctangent: tanh-1(.5)
5 & c 8 d
5 & c 8 e
.5 & c 8 f
2.00
0.67
0.86
0.86
0.20
-0.50
4.01
11.54
120.00
75.96
0.52
1.13
0.46
2.31
2.29
0.55
* 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
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.
Overview of Calculator Operations 9
-5
or 2
(1/3)
).
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.
Cr
n!
-----------------------------=
nr)! r!×–(
Permutations & m
The calculator computes the number of permutations of n items taken r
at a time. Both the
Pr
-------------------=
n and r variables must be greater than or equal to 0.
n!
nr)!–(
Rounding & o
The calculator computes using the rounded, displayed form of a number
instead of the internally stored value.
10 Overview of Calculator Operations
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 103, key in 3 < 10 ; 3.
Overview of Calculator Operations 11
Memory Operations
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 82.)
• 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).
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
To Pr es s
Clear memory 4 (by storing a zero value in it)
Store 14.95 in memory 3 (M3) 14.95 D 3
Recall a value from memory 7 (M7) J 7
0 D 4
Memory Arithmetic
Using memory arithmetic, you can perform a calculation with a stored
value and store the result with a single operation.
12 Overview of Calculator Operations
• 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.
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).
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 B 3
D ; 4
Calculations Using Constants
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.
Example: Multiply 3, 7, and 45 by 8
To Press Display
Clear the calculator. & U 0.00
Enter the value for the first calculation.
Enter the operation and a constant value. <
3
8 8
3
Store the operation and value, and then
calculate.
Calculate 7
Compute 45
Overview of Calculator Operations 13
Q 8.
Q 8.
& ` N 24.00
7 N 56.00
45 N 360.00
Keystrokes for Constant Calculations
This table shows how to create a constant for various operations.
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
*The letter c denotes the constant value.
**Repeat constant calculations with n N.
n B & ` c 2 N
Last Answer Feature
Use the Last Answer (
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 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.
ANS) feature with problems that call
Example: Using the Last Answer in a Calculation
To Press Display
Key in and complete a calculation
14 Overview of Calculator Operations
3 H 1 N 4.00
To Press Display
Key in a new calculation
Recall the last answer & x 4.00
Complete the calculation N 16.00
2 ; 2.00
Using Worksheets: Tools for Financial Solutions
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 standardcalculator mode, all variables are prompted.
For example, to assign values to amortization variables, you
must first press & \ to access the Amortization
worksheet.
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.
To select Function Press
TVM worksheet
(Chapter 2)
Amortization worksheet
(Chapter 2)
Cash Flow worksheet
(Chapter 3)
Bond worksheet
(Chapter 4)
Analyzes equal cash flows, for
example, annuities, loans,
mortgages, leases, and savings
Performs amortization
calculations and generates an
amortization schedule
Analyzes unequal cash flows by
calculating net present value
and internal rate of return
Computes bond price and yield
to maturity or call
,, -, .,
/, 0, or
& [
& \
& '
& l
Depreciation worksheet
(Chapter 5)
Overview of Calculator Operations 15
Generates a depreciation
schedule using one of six
depreciation methods
& p
To select Function Press
Statistics worksheet
(Chapter 6)
Analyzes statistics on one- or
two-variable data using four
& k
regression analysis options
Percent
Change/Compound
Interest worksheet
Computes percent change,
compound interest, and costsell markup
& q
(Chapter 7)
Interest Conversion
worksheet
(Chapter 7)
Converts interest rates
between nominal rate (or
annual percentage rate) and
& v
annual effective rate
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
Profit Margin worksheet
(Chapter 7)
Breakeven worksheet
(Chapter 7)
Computes cost, selling price,
and profit margin
Analyzes relationship between
fixed cost, variable cost, price,
profit, and quantity
Memory worksheet
(Chapter 7)
Accesses storage area for up to
10 values
Accessing the TVM Worksheet Variables
• 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 (
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.
& u
& w
& r
& {
xP/Y, P/Y,
16 Overview of Calculator Operations
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 (
).(See “TVM and Amortization Worksheet Variables” on page 22.)
INT
Indicators prompt you to select settings, enter values, or compute results.
For example, the i#
other variables. (See “Reading the Display” on page 2.)
To return to the standard-calculator mode, press & U.
$ indicators remind you to press # or " to select
P1, P2, BAL, PRN,
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
press ! after keying in a value to assign the value to the variable.
After you press !, the indicator confirms that the value is assigned.
ENTER indicator. The ENTER indicator reminds you to
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.
Overview of Calculator Operations 17
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
When you select an enter-or-compute variable, the calculator displays
the variable label with the ENTER and COMPUTE indicators.
YLD and PRI variables).
•The
•The COMPUTE indicator prompts you to press % to compute a
ENTER indicator prompts you to press ! to assign the keyed-
in value to the displayed variable.
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
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.
18 Overview of Calculator Operations
ACT/360 variable).
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.
Overview of Calculator Operations 19
20 Overview of Calculator Operations
2
Time-Value-of-Money and Amortization Worksheets
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.
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 & \.
Time-Value-of-Money and Amortization Worksheets 21
TVM and Amortization Worksheet Variables
Variable Key Display Type of Variable
Number of periods ,
Interest rate per year -
Present value .
Payment /
Future value 0
Number of payments per year & [
Number of compounding
#
periods per year
End-of-period payments & ]
Beginning-of-period
& V
payments
Starting payment & \
Ending payment #
Balance #
Principal paid #
Interest paid #
N
I/Y
PV
PMT
FV
P/Y
C/Y
END
BGN
P1
P2
BAL
PRN
INT
Enter-or-compute
Enter-or-compute
Enter-or-compute
Enter-or-compute
Enter-or-compute
Enter-only
Enter-only
Setting
Setting
Enter-only
Enter-only
Auto-compute
Auto-compute
Auto-compute
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 (
number, and press !. To change the compounding periods (C/Y),
press &[ #, key in a number, and press !.
• To change the payment period (
press & V.
• To compute a value for the unknown variable, press %, and then
press the key for the unknown variable.
22 Time-Value-of-Money and Amortization Worksheets
P/Y), press &[, key in a
END/BGN), press & ], and then
• 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 & } !:
Variable Default Variable Default
N
I/Y
PV
PMT
FV
P/Y
C/Y
0
0
0
0
0
1
1
• 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.
END/BGN END
P1
P2
BAL
PRN
INT
1
1
0
0
0
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 (
FV) with a known interest rate (I/Y) and no payments, enter 0 and
value (
PV) of a known future
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.
Time-Value-of-Money and Amortization Worksheets 23
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
(You can change
P/Y automatically enters the same value for C/Y.
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.
24 Time-Value-of-Money and Amortization Worksheets
• 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
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
Time-Value-of-Money and Amortization Worksheets 25
P1 and
6. Press & \.
— or —
INT is displayed, press # to display P1 again.
If
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
• If you press % with
displayed automatically. (You can still enter a new value for
• If you did not press % with
P2 displayed to enter values for both P1 and P2 in the next
with
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.
P2.
P1 displayed, a new value for P2 will be
P2.)
P1 displayed, you can press %
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 !
Return to standard-calculator
& U
mode.
Enter number of payments
30 & Z ,
using the payment multiplier.
26 Time-Value-of-Money and Amortization Worksheets
P/Y=
N=
12.00
0.00
360.00
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