Ba2plus BA II PLUS™ PROFESSIONAL Guidebook (English) PLUS PRO EN

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BA II PLUS
PROFESSIONAL Calculator
é

Important Information
Texas Instruments makes no warranty, either express or implied, including but
not limited to any implied warranties of merchantability and fitness for a
particular purpose, regarding any programs or book materials and makes
such materials available solely on an "as-is" basis.
In no event shall Texas Instruments be liable to anyone for special, collateral,
incidental, or consequential damages in connection with or arising out of the
purchase or use of these materials, and the sole and exclusive liability of Texas
Instruments, regardless of the form of action, shall not exceed the purchase
price of this product. Moreover, Texas Instruments shall not be liable for any
claim of any kind whatsoever against the use of these materials by any other
party.

Table of Contents
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

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

Cash Flow Worksheet ...........................................................41
Cash Flow Worksheet Variables................................................... 41
Uneven and Grouped Cash Flows................................................ 42
Entering Cash Flows ..................................................................... 43

Table of Contents

iii

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

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

Depreciation Worksheet ...................................................... 57
Depreciation Worksheet Variables .............................................. 57
Entering Data and Computing Results ........................................ 60
Example: Computing Straight-Line Depreciation ....................... 61

Statistics Worksheet............................................................. 63
Statistics Worksheet Variables ..................................................... 63
Regression Models ........................................................................ 65
Entering Statistical Data............................................................... 66

Other Worksheets................................................................. 69
Percent Change/Compound Interest Worksheet ........................ 69
Interest Conversion Worksheet.................................................... 73
Date Worksheet ............................................................................ 75
Profit Margin Worksheet ............................................................. 77
Breakeven Worksheet .................................................................. 78
Memory Worksheet ...................................................................... 80

APPENDIX - Reference Information ..................................... 83
Formulas ........................................................................................ 83
Error Messages .............................................................................. 92
Accuracy Information ................................................................... 94
AOS™ (Algebraic Operating System) Calculations ..................... 95
Battery Information...................................................................... 95
In Case of Difficulty ...................................................................... 96
Texas Instruments Support and Service ....................................... 98
Texas Instruments (TI) Warranty Information ............................. 98

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.

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 C 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.

1

The displayed value is entered in the selected worksheet.
The indicator clears following a computation.

7

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.

Overview of Calculator Operations

3

Setting Calculator Formats
You can change these calculator formats:
To Select

Press

Display

Defaul
t

Number of
decimal
places

& |

DEC 0–9 (Press 9 for

2

Angle units

#

floating-decimal)
DEG (degrees)

DEG

RAD (radians)

Dates

#

US (mm-dd-yyyy)

US

Eur (dd-mm-yyyy)

Number
separators

#

Calculation
method

#

US (1,000.00 )

US

Eur (1.000,00)
Chn (chain)

Chn

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.

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.
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”).

Pressing 2nd Reset
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.
To clear

Press

One character at a time, starting with the last digit *
keyed in
An incorrect entry, error condition, or error
message
6

P

Overview of Calculator Operations

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
standard-calculator mode

•

All pending operations in standard-calculator
mode

•

In a prompted worksheet, the variable value
keyed in but not entered (the previous value
appears)

•

Any calculation started but not completed

& U

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)

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

Begin the expression.

3<

Enter a number.

1234.86

Erase the entry error.

* *

Key in the correct number.

56

1,234.56

Compute the result.

N

3,703.68

Overview of Calculator Operations

Display
3.00
1,234.86
1,234.

7

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

Add 6 + 4

6H4N

10.00

Subtract 6 N 4

6B4N

2.00

Multiply 6 Q 4

6<4N

24.00

Divide 6 P 4

664N

1.50

3 ; 1.25 N

3.95

Find universal power: 3

1.25

Use parentheses: 7 Q (3 + 5)

Display

7< 93H5

56.00

: N
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

Find price with percent discount:
$69.99 N 10%
Square 6.3

2

Find number of combinations where:
n = 52, r = 5

34.86
532.86

N
69.99 B 10 2

N

7.00
62.99

6.3 4

39.69

52 & s 5 N

2,598,960.00

Find number of permutations where: 8 & m 3 N
n = 8, r = 3

336.00

These operations do not require you to press N to complete.
To

Press

Display

15.5 3

3.94

Find reciprocal: 1/3.2

3.2 5

0.31

Find factorial: 5!

5& g

Find square root:

8

15.5

120.00

Overview of Calculator Operations

To

Press

Find natural logarithm: ln 203.45

203.45 >

5.32

.69315 & i

2.00

Round 2 P 3 to the set decimal format

263N & 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

Find tangent:** tan(76°)

76 & f

Find natural antilogarithm: e

.69315

.2 8 d

-1

Find arcsine:** sin (.2)

.5 S 8 e

-1

Find arccosine:** cos (-.5)

48 f

-1

Find arctangent:** tan (4)

Display

-0.50
4.01
11.54
120.00
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

5& c 8 d

2.31

5& c 8 e

2.29

.5 & c 8 f

0.55

-1

Find hyperbolic arcsine: sinh (5)
-1

Find hyperbolic arccosine: cosh (5)
-1

Find hyperbolic arctangent: tanh (.5)
*

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”).

Universal Power ;
Press ; to raise the displayed postive 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.

Overview of Calculator Operations

9

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 zero

EXP

Y = a bx

All Y values > zero

PWR

Y = a Xb

All X and Y values > zero

The calculator interprets the X value as the independent variable and the
Y value as the dependent variable.
The calculator computes the statistical results using these transformed
values:
•

LIN uses X and Y.

Statistics Worksheet

65

•

Ln uses ln(X) and Y.

•

EXP uses X and ln(Y).

•

PWR uses ln(X) and ln(Y).

The calculator determines the values for a and b that create the line or
curve that best fits the data.

Correlation Coefficient
The calculator also determines r, the correlation coefficient, which
measures the goodness of fit of the equation with the data. Generally:
•

The closer r is to 1 or -1, the better the fit.

•

The closer r is to zero, the worse the fit.

Entering Statistical Data
Because the Statistics worksheet lets you enter and display up to 50 data
points, and then stores the values until you clear the worksheet or
change the values, you probably will not have to perform every step for
each Statistics calculation.
1. To select the data-entry portion of the Statistics worksheet, press &
j. X01 is displayed along with any previous value.
2. To clear the worksheet, press & z.
3. Key in a value for X01 and press !.
•

For one-variable data, X01 is the first data point.

•

For two-variable data, X01 is the first X value.

4. To display the Y01 variable, press #.
5. Key in a value for Y01 and press !.
•

For one-variable data, you can enter the number of times the X
value occurs (frequency).
The default value is 1.

•

For two-variable data, enter the first Y value.

6. To display the next X variable, press #.
7. Repeat steps 3 through 5 until you enter all of the data points.
Note: To easily scroll up or down through a range of variables, press and
hold # or ".
Computing Statistical Results
Selecting a Statistics Calculation Method
66

Statistics Worksheet

Press & k to select the statistical calculation portion of the Statistics
worksheet.
The last selected statistics calculation method is displayed (LIN, Ln, EXP,
PWR, or 1-V).
Press & V repeatedly until the statistics calculation method you want
is displayed.
If you are analyzing one-variable data, select 1-V.
Press # to begin computing results.
Computing Results
To compute results based on the current data set, press # repeatedly
after you have selected the statistics calculation method.
The calculator computes and displays the results of the statistical
calculations (except for X' and Y') automatically when you access them.
For one-variable statistics, the calculator computes and displays only the
values for n, v, Sx, sX, GX, and GX2.
Computing Y'
To select the Statistics worksheet, press & k.
Press " or # until X' is displayed.
Key in a value for X' and press !.
Press # to display the Y' variable.
Press C to compute a predicted Y' value.
Computing X'
To select the Statistics worksheet, press & k.
Press " or # until Y' is displayed.
Key in a value for Y' and press !.
Press " to display the X' variable.
Press C to compute an X' value.

Statistics Worksheet

67

68

Statistics Worksheet

Other Worksheets
The calculator also includes these worksheets:
•

Percent Change/Compound Interest worksheet
(& q)

•

Interest Conversion worksheet (& v)

•

Date worksheet (& u)

•

Profit Margin worksheet (& w)

•

Breakeven worksheet (& r)

•

Memory worksheet (& {)

Percent Change/Compound Interest Worksheet
Use the Percent Change/Compound Interest worksheet to
solve percent change, compound interest, and cost-sellmarkup problems.
•

To access the Percent Change/Compound Interest
worksheet, press & q.

•

To access the Percent Change/Compound Interest
variables, press # or ".

Percent Change/Compound Interest Worksheet Variables
Variable

Key

Display

Variable Type

Old value/Cost

&q

OLD

Enter/compute

New value/Selling price

#

NEW

Enter/compute

Percent change/Percent
markup

#

%CH

Enter/compute

Number of periods

#

#PD

Enter/compute

Note: This guidebook categorizes variables by their method of entry.
(See “Types of Worksheet Variables” on page 18.)

Other Worksheets

69

Resetting the Percent Change/Compound Interest
Worksheet Variables
•

•

To reset the Percent Change/Compound Interest variables to default
values, press & z while in the Percent Change/Compound
Interest worksheet.
Variable

Default

Variable

Default

OLD

0

OLD

0

NEW

0

NEW

0

To reset default values for all calculator variables and formats, press
& } !.

Entering Values
•

For percent-change calculations, enter values for any two of the three
variables (OLD, NEW, and %CH) and compute a value for the
unknown variable (leave #PD=1). A positive percent change
represents a percentage increase; a negative percent change
represents a percentage decrease.

•

For compound-interest calculations, enter values for the three known
variables and compute a value for the unknown fourth variable.

•

•

OLD= present value

•

NEW= future value

•

%CH= interest rate per period

•

#PD= number of periods

For cost-sell-markup calculations, enter values for two of the three
variables (OLD, NEW, and %CH) and compute a value for the
unknown.
•

OLD = cost

•

NEW= selling price

•

%CH= percent markup

•

#PD= 1

Computing Values
1. To select the Percent Change/Compound Interest worksheet, press &
q. The current value for OLD is displayed.
2. To clear the worksheet, press & z.

70

Other Worksheets

3. To enter values for the known variables, press # or " until the
variable you want is displayed, then key in a value, and press !.
(Do not enter a value for the variable you wish to solve.)
•

Percent Change — Enter values for two of these three variables:
OLD, NEW, and %CH. Leave #PD set to 1.

•

Compound Interest — Enter values for three of these four
variables: OLD, NEW, %CH, and #PD.

•

Cost-Sell-Markup — Enter values for two of these three
variables: OLD, NEW, and %CH. Leave #PD set to 1.

4. To compute a value for the unknown variable, press # or " until the
variable you want is displayed and press C. The calculator displays
the value.

Example: Computing Percent Change
First, determine the percentage change from a forecast amount of $658
to an actual amount of $700. Second, determine what the new amount
would be if it were 7% below the original forecast.
To

Press

Display

Select Percent Change/Compound
Interest worksheet.

&q

OLD=

Current
value

Enter original forecast amount.

658 !

OLD=

658.001

Enter actual amount.

# 700 !

NEW=

700.001

Compute percent change.

# C

%CH=

6.387

Enter -7 as percent change.

7S !

%CH=

-7.001

Compute new actual amount.

" C

NEW=

611.947

Answer: $700 represents a 6.38% increase over the original forecast of

$658. A decrease of 7% would result in a new actual amount of $611.94.

Example: Computing Compound Interest
You purchased stock in 1995 for $500. Five years later, you sell the stock
for $750. What was the annual growth rate?
To

Press

Select Percent Change/Compound & q
Interest worksheet.
Enter stock purchase price.
Other Worksheets

500 !

Display
OLD=

Current
value

OLD=

500.001
71

To

Press

Display

Enter stock selling price.

# 750 !

NEW=

Enter number of years.

# # 5 ! #PD=

5.001

Compute annual growth rate.

" C

8.457

%CH=

750.001

Answer: The annual growth rate is 8.45%.

Example: Computing Cost-Sell-Markup
The original cost of an item is $100; the selling price is $125. Find the
markup.
To

Press

Display

Select Percent Change/Compound
Interest worksheet.

& q

OLD=

Current
value

Clear worksheet variables.

& z OLD=

0.00

Enter original cost.

100 !

OLD=

100.001

Enter selling price.

# 125 !

NEW=

125.001

Compute percent markup.

# C

%CH=

25.007

Answer: The markup is 25%.

72

Other Worksheets

Interest Conversion Worksheet
The Interest Conversion worksheet converts interest rates
between nominal rate (or annual percentage rate) and
annual effective rate.
•

To access the Interest Conversion worksheet, press &
v.

•

To select interest conversion variables, press # or ".

Variable

Key

Display

Variable Type

Nominal rate

&v

NOM

Enter/compute

Annual effective rate

#

EFF

Enter/compute

Compounding periods per year #

C/Y

Enter-only

Note: The calculator categorizes variables by their method of entry. (See
“Types of Worksheet Variables” on page 18.)

Comparing the Nominal Interest Rate of Investments
Comparing the nominal interest rate (annual percentage rate) of
investments is misleading when the investments have the same nominal
rate but different numbers of compounding periods per year.
To make a more valid comparison, convert the nominal interest rate
(NOM) to the annual effective interest rate (EFF) for each investment.
•

The nominal interest rate (NOM) is the interest rate per compounding
period multiplied by the number of compounding periods per year.

•

The annual effective interest rate (EFF) is the compound annual
interest rate that you actually earn for the period of time stated.

Resetting Variables
•

To reset all calculator variables and formats to default values,
including the Interest Conversion worksheet variables, press
& } !.
Variable

Default

NOM

0

EFF

0

C/Y

1

Other Worksheets

73

•

To clear the NOM and EFF variables and reset default values without
affecting C/Y, press & z in the Interest Conversion
worksheet.

Converting Variables
You can convert a nominal rate to an annual effective rate or vice versa.

Entering Values for Nom and EFF
Enter a value for NOM or EFF as an annual rate.

Converting Interest Rates
1. To access the Interest Conversion worksheet, press & v. The
current NOM value appears.
2. To clear the worksheet, press & z.
3. Enter a value for the known interest rate (either NOM or EFF).
4. To enter a value for a known variable, press # or " until NOM or EFF
is displayed, key in a value, and press !.
5. Press # to display C/Y. If necessary, change the value and press !.
6. To compute a value for the unknown variable (interest rate), press #
or " until NOM or EFF is displayed, and then press ?. The calculator
displays the computed value.
Example: A bank offers a certificate that pays a nominal interest rate of
15% with quarterly compounding. What is the annual effective interest
rate?
To

Press

Display

Select Interest Conversion
worksheet.

& v

NOM=

Current
value

Enter nominal interest rate.

15 !

NOM=

15.001

Enter number of compounding
periods per year.

# # 4 ! C/Y=

Compute annual effective
interest rate.

" C

EFF=

4.001
15.877

Answer: A nominal interest rate of 15% compounded quarterly is
equivalent to an annual effective interest rate of 15.87%.

74

Other Worksheets

Date Worksheet
Use the Date worksheet to find the number of days
between two dates. You can also compute a date and day
of the week based on a starting date and a specified
number of days.
•

To access the Date worksheet, press & u.

•

To access the date variables, press # or ".

•

To select the day-count method (ACT and 360), press
& V once for each option.

Date Worksheet Variables
Variable

Key

Display

Variable Type

Date 1

& u

DT1

Enter/compute

Date 2

#

DT2

Enter/compute

Days between dates

#

DBD

Enter/compute

Actual/actual day-count method #

ACT*

Setting

30/360 day-count method

360*

Setting

#

Note: The calculator categorizes variables by their method of entry. (See
“Types of Worksheet Variables” on page 18.)

Resetting the Date Worksheet Variables
•

•

To reset default values for all calculator variables and formats,
including the Date worksheet variables, press & } !.
Variable

Default

Variable

Default

DT1

12-31-1990

DBD

0

DT2

12-31-1990

Day-count
method

ACT

To clear Date worksheet variables and reset default values without
affecting the day-count method, press & z while in the Date
worksheet.

Entering Dates
•

The calculator assumes that DT1 is earlier than DT2.

•

Enter dates for DT1 and DT2 in the selected US or European date
format.

Other Worksheets

75

•

When you compute a date for DT1 or DT2, the calculator displays a
three-letter abbreviation for the day of the week (for example, WED).

Selecting the Day-Count Method Affects Calculations
•

When you select ACT as the day-count method, the calculator uses
the actual number of days in each month and each year, including
adjustments for leap years.

•

When you select 360 as the day-count method, the calculator assumes
30 days per month (360 days per year). You can compute DBD using
this day-count method, but not DT1 or DT2.

Computing Dates
1. To select the Date worksheet, press & u. The DT1 value is
displayed.
2. To clear the worksheet, press & z.
3. Enter values for two of the three variables: DT1, DT2, and DBD.
Note: Do not enter a value for the variable you wish to solve for.
4. To enter a value for a variable, press # or " to display the variable.
5. Key in a value and press !.
6. To change the day-count method setting, press # until ACT or 360 is
displayed, and then press & V to select the other day-count
method.
7. To compute a value for the unknown variable, press # or " to display
the variable, and then press C. The calculator displays the
computed value.

Example: Computing Days between Dates
A loan made on September 4, 2003 defers the first payment until
November 1, 2003. How many days does the loan accrue interest before
the first payment?
To

Press

Display

Select Date worksheet.

& u

DT1=

12-31-1990

Enter first date.

9.0403 !

DT1=

9-04-20031

Enter second date.

# 11.0103 !

DT2=

11-01-20031

Select actual/actual day-count # #
method.

ACT

Compute days between dates. " C

DBD=

76

58.007

Other Worksheets

Answer: Because there are 58 days between the two dates, the loan
accrues interest for 58 days before the first payment.

Profit Margin Worksheet
The Profit Margin worksheet computes cost, selling price,
and gross profit margin.
Note: To perform markup calculations, use the Percent
Change/Compound Interest worksheet. (See “Percent
Change/Compound Interest Worksheet” on page 69.)
•

To access the Profit Margin worksheet, press & w.

•

To access profit margin variables, press " or #.

•

Enter values for the two known variables, and then
compute a value for the unknown variable.

Profit Margin Worksheet Variables
Variable

Key

Display

Variable Type

Cost

&w

CST

Enter/compute

Selling price

#

SEL

Enter/compute

MAR

Enter/compute

Profit margin #

Note: This guidebook categorizes calculator variables by their method of
entry. (See “Types of Worksheet Variables” on page 18.)

Gross Profit Margin and Markup
The terms margin and markup often are used interchangeably, but each
has a distinct meaning.
•

Gross profit margin is the difference between selling price and cost,
expressed as a percentage of the selling price.

•

Markup is the difference between selling price and cost, expressed as
a percentage of the cost.

Clearing Profit Margin Worksheet Variables
•

To clear the Profit Margin worksheet variables and reset default
values, press & z. All Profit Margin worksheet variables
default to zero.

•

To reset default values for all calculator variables and formats,
including the Profit Margin worksheet variables, press
& } !.

Other Worksheets

77

Computing Profit Margin
1. To select the Profit Margin worksheet, press & w. The CST value
appears.
2. To enter a value for one of the two known variables, press # or " to
select a variable, then key in a value and press !.
3. Repeat step 2 for the second known variable.
4. To compute a value for the unknown variable, press # or " to select
the variable and press C. The calculator displays the computed
value.

Example: Computing Profit Margin
The selling price of an item is $125. The gross profit margin is 20%. Find
the original cost.
To

Press

Display

Select Profit Margin worksheet.

&w

CST=

0.00

Enter selling price.

# 125 !

SEL=

125.001

Enter profit margin.

# 20 !

MAR=

Compute cost.

""C

CST=

20.001
100.00 7

Answer: The original cost is $100.

Breakeven Worksheet
The Breakeven worksheet computes the breakeven point
and sales level needed to earn a given profit by analyzing
relationships between fixed costs, variable costs per unit,
quantity, price, and profit.
You operate at a loss until you reach the breakeven
quantity (that is, total costs = total revenues).
•

To access the Breakeven worksheet, press & r.

•

To access breakeven variables, press " or #.

•

Enter known values for the four known variables, then
compute a value for the fifth, unknown variable.

Note: To solve for quantity (Q), enter a value of zero for profit (PFT).

78

Other Worksheets

Breakeven Worksheet Variables
Variable

Key

Display

Variable Type

Fixed cost

&
r

FC

Enter/compute

Variable cost per unit

#

VC

Enter/compute

Unit price

#

P

Enter/compute

Profit

#

PFT

Enter/compute

Quantity

#

Q

Enter/compute

Note: This guidebook categorizes calculator variables by their method of
entry. (See “Types of Worksheet Variables” on page 18.)

Resetting the Breakeven Worksheet Variables
•

To reset default values for all Breakeven worksheet variables, press
& z. All Breakeven worksheet variables default to zero.

•

To clear all calculator variables and formats and reset default values,
including the Breakeven worksheet variables, press & } !.

Computing Breakeven
1. To access the Breakeven worksheet, press & r. The FC variable
appears.
2. Press # or " to select a known variable, key in the value, and press
!.
3. Repeat step 3 for each of the remaining known variables.
4. To compute a value for the unknown variable, press # or " until the
variable is displayed, and then press C The calculator displays the
computed value.

Example: Computing Breakeven Quantity
A canoe company sells paddles for $20 each. The unit variable cost is $15,
and the fixed costs are $3,000. How many paddles must be sold to break
even?
To

Press

Display

Access Breakeven worksheet.

&r

FC=

Current value

Enter fixed costs.

3000 !

FC=

3,000.001

Enter variable cost per unit.

# 15 !

VC=

15.001

Enter price.

# 20 !

P=

20.001

Other Worksheets

79

To

Press

Display

Leave profit as is.

#

PFT=

Compute quantity.

#C

Q=

0.00
600.007

Answer: 600 paddles must be sold to break even.

Memory Worksheet
The Memory worksheet lets you compare and recall stored
values by accessing the calculator’s 10 memories. All
memory variables are enter-only. (See “Types of Worksheet
Variables” on page 18.)
•

To access the Memory worksheet, press & {.

•

To access memory variables, press " or #.
Note: You can access memories individually using D,
J, and the digit keys. (See “Memory Operations” on
page 12.)

Memory Worksheet Variables
Variables

Key

Display

Variable Type

Memory 0

&{

M0

Enter-only

Memory 1

#

M1

Enter-only

Memory 2

#

M2

Enter-only

Memory 3

#

M3

Enter-only

Memory 4

#

M4

Enter-only

Memory 5

#

M5

Enter-only

Memory 6

#

M6

Enter-only

Memory 7

#

M7

Enter-only

Memory 8

#

M8

Enter-only

Memory 9

#

M9

Enter-only

Note: This guidebook categorizes calculator variables by their method of
entry. (See “Types of Worksheet Variables” on page 18.)

80

Other Worksheets

Clearing the Memory Worksheet Variables
To clear all 10 memories at once, press & z in the Memory
worksheet.

Using the Memory Worksheet
1. To select the Memory worksheet, press & {. M0 apears.
2. Perform any of the following operations:
•

To clear all 10 memories at once, press & z.

•

To view the contents of the memories, press # or " once for each
memory.

•

To store a value, select a memory (M0-M9), key in a value, and
press !.

•

Memory arithmetic. (See “Memory Arithmetic” on page 12.)

Examples: Using the Memory Worksheet
To

Press

Display

Access Memory worksheet

& {

M0=

Current value

Select M4.

####

M4=

Current value

Clear M4.

0!

M4=

0.001

Store 95.

95!

M4=

95.001

Add 65.

H65!

M4=

160.001

Subtract 30.

B30!

M4=

130.001

Multiply by 95.

<95!

M4=

12,350.001

Divide by 65.

665!

M4=

190.001

Raise to 2nd power.

;2!

M4=

36,100.001

Other Worksheets

81

82

Other Worksheets

APPENDIX - Reference Information
This appendix includes supplemental information to help you use your
BA II PLUSé PROFESSIONAL calculator:
•

Formulas

•

Error conditions

•

Accuracy information

•

IRR (internal-rate-of-return) calculations

•

Algebraic operating system (AOS™)

•

Battery information

•

In case of difficulty

•

TI product service and warranty information

Formulas
This section lists formulas used internally by the calculator.

Time Value of Money

i  e( y  ln ( x  1))   1 i =  e  y  ln  x + 1    – 1
where: PMT ?Ä0
y =C/Y P P/Y
x =(.01 Q I/Y) P C/Y
C/Y =compounding periods per year
P/Y =payment periods per year
I/Y =interest rate per year

i =  – FV  PV 

1  N

–1

where: PMT =0
The iteration used to compute i:
–N

1 – 1 + i
–N
0 = PV + PMT  G i ------------------------------ + FV   1 + i 
i

APPENDIX - Reference Information

83

I/Y = 100  C  Y   e

 y  ln  x + 1  

– 1

where: x = i
y =P/Y P C/Y

Gi = 1 + i Q k
where: k =0 for end-of-period payments
k =1 for beginning-of-period payments

PMT  G i – FV  i 
ln  --------------------------------------------- PMT  G i + PV  i
N = ---------------------------------------------------------ln  1 + i 
where: i ?0

N = L(PV + FV) P PMT
where: i =0

–i
PV + FV PMT = -----  PV + --------------------------N
Gi
1 + i – 1
where: i ?0

PMT = L(PV + FV) P N
where: i =0

PMT  G i
PMT  G i
1
PV = ------------------------ – FV  ------------------N- – -----------------------i
i
1 + i
where: i ?0

84

APPENDIX - Reference Information

PV = L(FV + PMT Q N)
where: i =0

PMT  G
PMT  G
N
FV = ------------------------i –  1 + i    PV + ------------------------i


i
i
where: i ?0

FV = L(PV + PMT Q N)
where: i =0

Amortization
If computing bal(), pmt2 = npmt
Let bal(0) = RND(PV)
Iterate from m = 1 to pmt2

I m = RND  RND12  – i  bal  m – 1   
 bal  m  = bal  m – 1  – I m + RND  PMT 
then:

bal( ) =bal(pmt2)
GPrn( ) =bal(pmt2) N bal(pmt1)
GInt( ) =(pmt2 N pmt1 +1) Q RND(PMT) N GPrn( )

where: RND =round the display to the number of decimal
places selected
RND12 =round to 12 decimal places
Balance, principal, and interest are dependent on the values of PMT, PV, I/
Y, and pmt1 and pmt2.

Cash Flow
N

NPV = CF 0 +

 CFj  1 + i 

-S – 1 1
j

j=1

APPENDIX - Reference Information

-n

– 1 + i j
---------------------------------i

85

 j
ni

where:S j =  
i = 1
 0

j1
j = 0

Net present value depends on the values of the initial cash flow (CF0),
subsequent cash flows (CFj), frequency of each cash flow (nj), and the
specified interest rate (i).

p

NFV =  1 + i   NPV
where: i is the periodic interest rate used in the calculation of NPV.
N

p =

 nk
k=1

where: n k is the frequency of the kth cash flow.

IRR = 100  i, where i satisfies npv() = 0
Internal rate of return depends on the values of the initial cash flow
(CF0) and the subsequent cash flows (CFj).

i = I/Y  100

The calculator uses this formula to compute the modified internal rate of
return:

– NPV (positive, rrate
MOD = ----------------------------------------------------NPV (negative, frate)

1N

  1 + rrate  – 1

where: positive = positive values in the cash flows
negative = negative values in the cash flows
86

APPENDIX - Reference Information

N = number of cash flows
rrate = reinvestment rate
frate = finance rate
NPV (values, rate) = Net present value of the values in the rate
described

Bonds1
Price (given yield) with one coupon period or less to redemption:

100  R
RV + -----------------M
A 100  R
PRI = --------------------------------------- – ---  -----------------E
M
DSR Y
1 +  -----------  ----- 

 E
M
where: PRI =dollar price per $100 par value
RV =redemption value of the security per $100 par value (RV =
100 except in those cases where call or put features must be
considered)
R =annual interest rate (as a decimal; CPN _ 100)
M =number of coupon periods per year standard for the
particular security involved (set to 1 or 2 in Bond worksheet)
DSR =number of days from settlement date to redemption date
(maturity date, call date, put date, etc.)
E =number of days in coupon period in which the settlement
date falls
Y =annual yield (as a decimal) on investment with security held
to redemption (YLD P 100)
A =number of days from beginning of coupon period to
settlement date (accrued days)
Note: The first term computes present value of the redemption amount,
including interest, based on the yield for the invested period. The second
term computes the accrued interest agreed to be paid to the seller.

1.Source for bond formulas (except duration): Lynch, John J.,
Jr., and Jan H. Mayle. Standard Securities Calculation Methods. New York: Securities Industry Association, 1986.
APPENDIX - Reference Information

87

Yield (given price) with one coupon period or less to redemption:

RV R   PRI  A R  
 -------- + ----- – ---------- + ---  ---- 100 M  100  E M 
ME
Y = ---------------------------------------------------------------------------  -------------DSR
PRI  A R 
---------- + ---  ----100  E M
Price (given yield) with more than one coupon period to redemption:

RV
-----------------------------------------DSC
N – 1 + -----------Y
E
PRI =  1 + -----
+
M
R A
– 100  -----  --M E

N



R
100  ----M
------------------------------------------Y
1 + -----

M

K = 1

DSC
K – 1 + -----------E

where: N =number of coupons payable between settlement date and
redemption date (maturity date, call date, put date, etc.). (If this
number contains a fraction, raise it to the next whole number;
for example, 2.4 = 3)
DSC =number of days from settlement date to next coupon date
K =summation counter
Note: The first term computes present value of the redemption amount,
not including interest. The second term computes the present values for
all future coupon payments. The third term computes the accrued
interest agreed to be paid to the seller.

Yield (given price) with more than one coupon period to redemption:
Yield is found through an iterative search process using the “Price with
more than one coupon period to redemption” formula.

88

APPENDIX - Reference Information

Accrued interest for securities with standard coupons or interest at
maturity:

R A
AI = PAR  -----  --M E
where: AI =accrued interest
PAR =par value (principal amount to be paid at maturity)

Modified duration:1

Duration
Modified Duration = -----------------------Y
1 + ----M
where Duration is calculated using one of the following formulas used to
calculate Macaulay duration:
•

For a bond price with one coupon period or less to redemption:

Y
Dur =  1 + -----

M
•

100  R
Rv + -----------------M
Dsr  -----------------------------------------2Dsr  Y
1 +  -------------------
 EM 
 ---------------------------------------------------------------E  M  Pri

For a bond price with more than one coupon period to redemption:

Dsc
Rv   N – 1 + ----------

E 
------------------------------------------------ +
Dsc
N + ----------

Y
Dur =  1 + -----

M

N



R
Dsc
100  -----   k – 1 + ----------
M 
E 
-----------------------------------------------------------Dsc
k + ----------

E
E
k=1
Y
Y
 1 + --- 1 + ---



M
M
 ---------------------------------------------------------------------------------------------------------------------------------------M  Pri

1.Source for duration: Strong, Robert A., Portfolio Construction, Management, and Protection, South-Western College
Publishing, Cincinnati, Ohio, 2000.
APPENDIX - Reference Information

89

Note: Bond price formulas and notations are described in this section.

Depreciation
RDV = CST N SAL N accumulated depreciation
Values for DEP, RDV, CST, and SAL are rounded to the number of
decimals you choose to be displayed.
In the following formulas, FSTYR = (13 N MO1) P 12.

Straight-line depreciation

CST – SAL
--------------------------LIF
CST – SAL
LIF

First year: ---------------------------  FSTYR
Last year or more: DEP = RDV

Sum-of-the-years’-digits depreciation

LIF + 2 – YR – FSTYR    CST – SAL ----------------------------------------------------------------------------------------------------  LIF   LIF + 1    2 
LIF   CST – SAL 
  LIF   LIF + 1    2 

First year: ------------------------------------------------------------  FSTYR
Last year or more: DEP = RDV

Declining-balance depreciation

RBV  DB%
------------------------------LIF  100
where: RBV is for YR - 1

CST  DB%
LIF  100

First year: -------------------------------  FSTYR

CST  DB%
LIF  100

Unless -------------------------------  RDV ; then use RDV Q FSTYR
If DEP > RDV, use DEP = RDV
If computing last year, DEP = RDV
90

APPENDIX - Reference Information

Statistics
Note: Formulas apply to both x and y.
Standard deviation with n weighting (s x):



2


x


x 2 – -------------------n
----------------------------------------n



12

Standard deviation with n-1 weighting (s x):



2


x


x 2 – -------------------n
----------------------------------------n–1



12

 x 

Mean: x = ---------------

n

Regressions
Formulas apply to all regression models using transformed data.

n   xy  –   y    x 
b = -------------------------------------------------------2
n   x2  –   x 
 y – b x
a = --------------------------------n
b
r = --------x
y

APPENDIX - Reference Information

91

Interest Rate Conversions

EFF = 100   e C  Y  In  x  1  – 1 
where: x =.01 Q NOM P C?Y

NOM = 100  C  Y   e 1  C  Y  In  x + 1  – 1 
where: x =.01 Q EFF

Percent Change

%CH
NEW = OLD  1 + --------------

100 

#PD

where: OLD =old value
NEW =new value
%CH =percent change
#PD =number of periods

Profit Margin

Selling Price – Cost
Gross Profit Margin = ------------------------------------------------  100
Selling Price
Breakeven
PFT = P Q N (FC + VC Q)
where: PFT =profit
P =price
FC =fixed cost
VC =variable cost
Q =quantity

Days between Dates
With the Date worksheet, you can enter or compute a date within the
range January 1, 1950, through December 31, 2049.

Actual/actual day-count method
Note: The method assumes the actual number of days per month and
per year.
92

APPENDIX - Reference Information

DBD (days between dates) = number of days II - number of days I
Number of Days I= (Y1 - YB) Q 365
+ (number of days MB to M1)
+ DT1

 Y1 – YB 
4

+------------------------

Number of Days II=(Y2 - YB) Q 365
+ (number of days MB to M2)
+ DT2

 Y2 – YB 
4

+ ------------------------

where: M1 =month of first date
DT1 =day of first date
Y1 =year of first date
M2 =month of second date
DT2 =day of second date
Y2 =year of second date
MB =base month (January)
DB =base day (1)
YB =base year (first year after leap year)

30/360 day-count method1
Note: The method assumes 30 days per month and 360 days per year.

DBD =  Y2 – Y1   360 +  M2 + M1   30 +  DT2 – DT1 
where: M1 =month of first date
DT1 =day of first date
Y1 =year of first date
M2 =month of second date
DT2 =day of second date
Y2 =year of second date
Note: If DT1 is 31, change DT1 to 30. If DT2 is 31 and DT1 is 30 or 31,
change DT2 to 30; otherwise, leave it at 31.

1.Source for 30/360 day-count method formula: Lynch, John
J., Jr., and Jan H. Mayle. Standard Securities Calculation
Methods. New York: Securities Industry Association, 1986
APPENDIX - Reference Information

93

Error Messages
Note: To clear an error message, press P.
Error

Possible Causes

Error 1

•

A result is outside the calculator range
( 9.9999999999999E99).

•

Tried to divide by zero (can occur internally).

•

Tried to compute 1/x when x is zero.

•

Statistics worksheet: a calculation included X or Y
values that are all the same.

Error 2

•

Tried to compute x! when x is not an integer 0-69.

Invalid
argument

•

Tried to compute LN of x when x is not > 0.

•

Tried to compute y x when y < 0 and x is not an
integer or the inverse of an integer.

•

Tried to compute

Overflow

•

x when x < 0.

Amortization worksheet: tried to compute BAL,
PRN, and INT when P2 < P1.

•

Depreciation worksheet: a calculation included
SAL > CST.

Error 3

•

Too many
pending
operations

More than 15 active levels of parentheses were
tried in a calculation.

•

A calculation tried to use more than 8 pending
operations.

Error 4

•

Amortization worksheet: the value entered for P1
or P2 is outside the range 1-9,999.

Out of range

94

•

TVM worksheet: the P/Y or C/Y value ? 0.

•

Cash Flow worksheet: the Fnn value is outside the
range 0.5-9,999.

•

Bond worksheet: the RV, CPN, or PRI value ?_0.

•

Date worksheet: the computed date is outside the
range January 1, 1950 through December 31, 2049.

•

Depreciation worksheet: the value entered for:
declining balance percent ? 0; LIF ? 0; YR _?0; CST < 0;
SAL < 0; or M01 1 ? M01 ? 13.

•

Interest Conversion worksheet: the C/Y value ? 0.

•

The DEC value is outside the range 0-9.

APPENDIX - Reference Information

Error

Possible Causes

Error 5

•

No solution
exists

TVM worksheet: the calculator computed I/Y when
FV, (N Q PMT), and PV all have the same sign.
(Make sure cash inflows are positive and outflows
are negative.)

•

TVM, Cash Flow, and Bond worksheets: the LN
(logarithm) input is not > 0 during calculations.

•

Cash Flow worksheet: the calculator computed IRR
without at least one sign change in the cash-flow
list.

•

Bond and Date worksheets: a date is invalid (for
example, January 32) or in the wrong format (for
example, MM.DDYYYY instead of MM.DDYY.

•

Bond worksheet: the calculator attempted a
calculation with a redemption date earlier than or
the same as the settlement date.

Error 7

•

Iteration limit
exceeded

TVM worksheet: the calculator computed I/Y for a
very complex problem involving many iterations.

•

Cash Flow worksheet: the calculator computed IRR
for a complex problem with multiple sign changes
or PB/DPB with no payback period based on input
cash flow values.

•

Bond worksheet: the calculator computed YLD for
a very complex problem.

Error 8

•

Canceled
iterative
calculation

TVM worksheet: $ was pressed to stop the
evaluation of I/Y.

•

Amortization worksheet: $ was pressed to
stop the evaluation of BAL or INT.

•

Cash Flow worksheet: $ was pressed to stop
the evaluation of IRR.

•

Bond worksheet: $ was pressed to stop the
evaluation of YLD.

•

Depreciation worksheet: $ was pressed to stop
the evaluation of DEP or RDV.

Error 6

Invalid date

Accuracy Information
The calculator stores results internally as 13-digit numbers but displays
them rounded to 10 digits or fewer, depending on the decimal format.
The internal digits, or guard digits, increase the calculator’s accuracy.
Additional calculations use the internal value, not the value displayed.
APPENDIX - Reference Information

95

Rounding
If a calculation produces a result with 11-digits or more, the calculator
uses the internal guard digits to determine how to display the result. If
the eleventh digit of the result is 5 or greater, the calculator rounds the
result to the next larger value for display.
For example, consider this problem.
1P3Q3=?
Internally, the calculator solves the problem in two steps, as shown
below.
1. 1 P 3 = 0.3333333333333
2. 0.3333333333333 Q 3 = 0.9999999999999
The calculator rounds the result and displays it as 1. This rounding
enables the calculator to display the most accurate result.
Although most calculations are accurate to within ±1 in the last displayed
digit, higher-order mathematical functions use iterative calculations, in
which inaccuracies can accumulate in the guard digits. In most cases, the
cumulative error from these calculations is maintained beyond the 10digit display so that no inaccuracy is shown.

AOS™ (Algebraic Operating System) Calculations
When you select the AOS calculation method, the calculator uses the
standard rules of algebraic hierarchy to determine the order in which it
performs operations.

Algebraic Hierarchy
The table shows the order in which the calculator performs operations
using the AOS calculation method.
Priority

Operations

1 (highest)

x2, x!, 1/x, %, ?x, LN, e2, HYP, INV, SIN, COS, TAN

2

nCr, nPr

3

Yx

4

Q, P

5

+, -

6

)

7 (lowest)

=

96

APPENDIX - Reference Information

Battery Information
Replacing the Battery
Replace the battery with a new CR2032 lithium battery.
Caution: The calculator cannot retain data when the battery is removed
or discharged. Replacing the battery has the same effect as resetting the
calculator.
1. Turn off the calculator and turn it over with the back facing you.
2. Slide the battery cover up and remove it from the back case.
3. Remove the battery.
4. Install the new battery with the positive sign (+) sign showing.
5. Replace the battery cover.

Battery Precautions
•

Do not leave batteries within the reach of children.

•

Do not mix new and used batteries. Do not mix brands (or types
within brands) of batteries.

•

Do not mix rechargeable and nonrechargeable batteries.

•

Install batteries according to polarity (+ and –) diagrams.

•

Do not place nonrechargeable batteries in a battery recharger.

•

Properly dispose of used batteries immediately.

•

Do not incinerate or dismantle batteries.

APPENDIX - Reference Information

97

In Case of Difficulty
Use this list of possible solutions to difficulties you might encounter with
the calculator to determine if you can correct a problem before having to
return it for service.
Difficulty

Solution

The calculator computes
wrong answers.

Check the settings of the current
worksheet to make sure they are
correct for the problem you are
working; for example, in the TVM
worksheet, check END and BGN and be
sure the unused variable is set to zero.

The display is blank; digits do
not appear.

Select the worksheet again. Be sure the
battery is properly installed and
replace, if necessary.

The calculator does not display Be sure you have selected the correct
the correct worksheet
worksheet.
variables.
The calculator does not display Press & | to check or adjust the
the correct number of decimal setting for number of decimal places
places.
displayed.
The calculator does not display Press & | # # to check or
the correct date format.
adjust the setting for date format.
The calculator does not display Press & | # # # to check or
the correct separator format. adjust the setting for separator format.
The calculator does not display Press & | # # # # to check
the correct result in a math
or adjust the setting for calculation
calculation.
method.
An error occurs.

(See “Error Messages” on page 92.)

If you experience difficulties other than those listed above, press
& } ! to clear the calculator, and then repeat your
calculations.
Note: You can also perform a hard reset using the reset hole in back of
the calculator. (See “Resetting the Calculator” on page 6.)

98

APPENDIX - Reference Information

Texas Instruments Support and Service
For general information
Home Page:

education.ti.com

KnowledgeBase
and e-mail
inquiries:

education.ti.com/support

Phone:

(800) TI-CARES / (800) 842-2737
For U.S., Canada, Mexico, Puerto Rico, and
Virgin Islands only

International
Information:

education.ti.com/support
(Click the International Information link.)

For technical support
KnowledgeBase
and support by
e-mail:

education.ti.com/support

Phone
(not toll-free):

(972) 917-8324

For TI-Navigator™ Technical Questions
E-mail:

ti-navigator@ti.com

Phone:

(866) TI-NAVIGATOR / (866) 846-2844

For Product (hardware) Service
Customers in the U.S., Canada, Mexico, Puerto Rico and Virgin
Islands: Always contact Texas Instruments Customer Support before
returning a product for service.
All other customers: Refer to the leaflet enclosed with this product
(hardware) or contact your local Texas Instruments retailer/distributor.

Texas Instruments (TI) Warranty Information
Customers in the U.S. and Canada Only
One-Year Limited Warranty for Commercial Electronic
Product

APPENDIX - Reference Information

99

This Texas Instruments (“TI”) electronic product warranty extends only to
the original purchaser and user of the product.

Warranty Duration. This TI electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase
date.
Warranty Coverage. This TI electronic product is warranted against
defective materials and construction. THIS WARRANTY IS VOID IF THE
PRODUCT HAS BEEN DAMAGED BY ACCIDENT OR UNREASONABLE USE,
NEGLECT, IMPROPER SERVICE, OR OTHER CAUSES NOT ARISING OUT OF
DEFECTS IN MATERIALS OR CONSTRUCTION.

Warranty Disclaimers. ANY IMPLIED WARRANTIES ARISING OUT OF THIS
SALE, INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE LIMITED IN
DURATION TO THE ABOVE ONE-YEAR PERIOD. TEXAS INSTRUMENTS SHALL
NOT BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL OR
CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY THE CONSUMER OR ANY OTHER USER.

Some states/provinces do not allow the exclusion or limitation of
implied warranties or consequential damages, so the above limitations or exclusions may not apply to you.
Legal Remedies. This warranty gives you specific legal rights, and you
may also have other rights that vary from state to state or province to
province.
Warranty Performance. During the above one (1) year warranty
period, your defective product will be either repaired or replaced with a
reconditioned model of an equivalent quality (at TI’s option) when the
product is returned, postage prepaid, to Texas Instruments Service Facility. The warranty of the repaired or replacement unit will continue for
the warranty of the original unit or six (6) months, whichever is longer.
Other than the postage requirement, no charge will be made for such
repair and/or replacement. TI strongly recommends that you insure the
product for value prior to mailing.
Software. Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific
requirements. All software is provided “AS IS.”

100

APPENDIX - Reference Information

Copyright. The software and any documentation supplied with this
product are protected by copyright.

Australia & New Zealand Customers only
One-Year Limited Warranty for Commercial Electronic
Product
This Texas Instruments electronic product warranty extends only to the
original purchaser and user of the product.
Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the
original purchase date.
Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction. This warranty is
void if the product has been damaged by accident or unreasonable use,
neglect, improper service, or other causes not arising out of defects in
materials or construction.
Warranty Disclaimers. Any implied warranties arising out of this
sale, including but not limited to the implied warranties of merchantability and fitness for a particular purpose, are limited in
duration to the above one-year period. Texas Instruments shall
not be liable for loss of use of the product or other incidental or
consequential costs, expenses, or damages incurred by the consumer or any other user.
Except as expressly provided in the One-Year Limited Warranty
for this product, Texas Instruments does not promise that facilities for the repair of this product or parts for the repair of this
product will be available.
Some jurisdictions do not allow the exclusion or limitation of implied
warranties or consequential damages, so the above limitations or exclusions may not apply to you.
Legal Remedies. This warranty gives you specific legal rights, and you
may also have other rights that vary from jurisdiction to jurisdiction.

APPENDIX - Reference Information

101

Warranty Performance. During the above one (1) year warranty
period, your defective product will be either repaired or replaced with a
new or reconditioned model of an equivalent quality (at TI’s option)
when the product is returned to the original point of purchase. The
repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than your cost to
return the product, no charge will be made for such repair and/or
replacement. TI strongly recommends that you insure the product for
value if you mail it.
Software. Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific
requirements. All software is provided “AS IS.”
Copyright. The software and any documentation supplied with this
product are protected by copyright.

All Other Customers
For information about the length and terms of the warranty, refer to
your package and/or to the warranty statement enclosed with this product, or contact your local Texas Instruments retailer/distributor.

102

APPENDIX - Reference Information

Index
– (negative) indicator 3

Symbols
( (mean of X) 63, 65
( (mean of Y) 63
(x (population standard deviation of
X) 63, 65
(X (sum of X) 63, 65
(X2 (sum of X2) 63, 65
(XY (sum of XY products) 63
(y (population standard deviation of
Y) 63
(Y (sum of Y) 63
(Y2 (sum of Y2) 63
* (value computed) indicator 3
# $ indicator 3
#PD (number of periods, Percent
Change/Compound Interest
worksheet) 70
#PD (number of periods) 70, 71, 72
%CH (percent change) 70, 71, 72
= (value assigned) indicator 3

Numerics
1/Y (one coupon per year) 52, 53, 55
1-V (one-variable statistics ) 63, 65
2/Y (two coupons per year) 52, 53, 55
2nd (second)
functions 2
indicator 3
30/360 day-count method (360) 52,
53, 55, 76
360 (30/360 day-count method) 52,
53, 55, 76

A
Ä (value entered) indicator 3
a (y-intercept) 63
Accrued interest (AI) 52, 55, 56
Accuracy 94
ACT (actual/actual day-count
method) 52, 53, 55, 76

Index

Actual/actual (ACT) day-count
method 76
Actual/actual day-count method
(ACT) 52, 53, 55
Addition 8
AI (accrued interest) 52, 55, 56
Algebraic Operating System (AOS™)
calculations 4, 5, 95
Amortization
formulas 85
schedule 21, 25, 26, 38
worksheet 21
Amount of nth cash flow (Cnn) 41
Angle units format 5
Annual coupon rate, percent (CPN)
52, 54, 55
Annual effective rate (EFF) 74
annual interest rate 54, 73, 86
Annuities 21
due 24, 29, 30
ordinary 24, 29, 30
perpetual 30
ANS (Last Answer) feature 14
AOS™ (Algebraic Operating System)
calculations 5, 95
APD™ (Automatic Power Down™)
feature 1, 2
Arccosine 9
Arcsine 9
Arctangent 9
Automatic Power Down™ (APD™)
feature 1, 2

B
b (slope) 63
Backspace key 7
BAL (balance) 22, 24
Balance (BAL) 22, 24
Battery 95
precautions 96
replacing 95
Beginning-of-period (BGN)
indicator 3
payments 22, 24
103

BGN (beginning-of-period)
indicator 3
payments 22, 24
Bond
accrued interest (AI) 52
price (PRI) 56
terminology 54
worksheet 51–56
Breakeven worksheet 78–80

C
C/Y (compounding periods per year)
22, 24, 74
Calculation method 4, 5
Call date 54
Cash Flow worksheet 41–50
Cash flows
computing 44
deleting 42, 43
editing 47
entering 42, 43
formulas 85
grouped 43
inserting 44
uneven 42
CFo (initial cash flow) 41
Chain (Chn) calculation 4, 5, 8
Chn (chain) calculation 4, 5, 8
Clearing
calculations 6
calculator 6
characters 6
entry errors 6
error messages 6
errors 6
memory 6, 12
worksheets 6
Cnn (amount of nth cash flow) 41
Combinations 8, 10
Compound interest 54, 69, 71, 73
Compounding periods per year (C/Y)
22, 24, 74
COMPUTE indicator 3
Constant Memory™ feature 2
Constants 13
contact information 98
Correcting entry errors 7

104

Correlation coefficient (r) 63, 66
Cost (CST) 57, 60, 77, 78
Cost-Sell-Markup 71, 72
Coupon payment 54
CPN (annual coupon rate, percent)
52, 53, 54, 55
CST (cost) 57, 60, 77, 78
Curve fitting 65
customer support and service 98
CV_Cash Flow Variables 41

D
Data points 66
Date 1 and 2 (DT1, DT2) 57, 76
Date worksheet 75
Dates
30/360 day-count method (360)
76
actual/actual (ACT) day-count
method 76
date 1 and 2 (DT1, DT2) 76
days between dates (DBD) 76
entering 75
Days between dates (DBD) 76
DB (declining balance) 57, 59, 60, 89
DBD (days between dates) 76
DBF (French declining balance) 57,
59, 60
DBX (declining balance with
crossover) 57, 59, 60
DEC (decimal format) 4
Decimal format (DEC) 4
Declining balance (DB) 57, 59, 60, 89
Declining balance with crossover
(DBX) 57, 59, 60
DEG (degrees) 4, 5
Degree angle units 5
Degrees (DEG) 4, 5
DEL (delete) indicator 3
Delete (DEL) indicator 3
DEP (depreciation) 57, 58, 60
Depreciation (DEP) 57, 58, 60
Depreciation worksheet 57–61
Difficulty 96
Discount bond 54
Discount rate (I) 41
Display indicators 3

Index

Division 8
Dollar price (PRI) 52, 54, 55
DT1 (starting date) 60
DT1, DT2 (date 1 and 2) 57, 76
DUR (modified duration) 52

E
EFF (annual effective rate) 74
END (end-of-period)
payments 22, 24
Ending payment (P2) 22, 24
End-of-period (END)
payments 22, 24
ENTER indicator 3
Error
clearing 92
messages 92
Examples
accrued interest 56
amortization schedule 38
amount to borrow 36
annuities 30
balloon payment 40
bond price 56
compound interest 71
computing basic loan payments
27
constants 13
converting interest 74
correcting an entry error 7
cost-sell-markup 72
days between dates 76
down payment 36
editing cash flow data 47
entering cash flow data 47
future value (savings) 28
interest received 40
internal rate of return 48
last answer 14
lease with uneven payments 48
memory 12
Memory worksheet 81
modified duration 56
monthly payments 40
monthly savings deposits 35
mortgage payments 38

Index

net present value 47, 48, 49
other monthly payments 34
percent change 71
perpetual annuities 30
present value (annuities) 29
present value (lease with
residual value) 33
present value (savings) 28
present value (variable cash
flow) 33
profit margin 78
regular deposits for specific
goals 37
remaining balance (balloon
payment) 40
residual value 33
saving for future 35
straight-line depreciation 61
EXP (exponential regression) 63, 65
Exponential regression (EXP) 63, 65

F
Face value 54
Factorial 10
FC (fixed cost) 79
Fixed cost (FC) 79
Floating-decimal format 4
Fnn (frequency of nth cash flow) 41
Forecasting 65
Formats
angle units 4, 5
calculation method 5
decimal places 4
number separators 4
setting 4
Formulas
30/360 day-count method 91
accrued interest 88
actual/actual day-count method
91
amortization 85
bond price (more than one
coupon period to
redemption) 87
bond price (one coupon period
or less to redemption) 86

105

bond yield (more than one
coupon period to
redemption) 88
bond yield (one coupon period
or less to redemption) 87
bonds 86
breakeven 90
cash flow 85
days between dates 91
depreciation 88
depreciation, declining-balance
89
depreciation, straight-line 88
depreciation, sum-of-the-years’digits 88
interest-rate conversions 90
internal rate of return 86
net present value 85
percent change 90
profit margin 90
regressions 89
statistics 89
time-value-of-money 83
French declining balance (DBF) 57,
59, 60
French straight line (SLF) 57, 59, 60
Frequency 44
cash flow 86
coupon 53, 55
one-variable data 66
Y value 63, 65
Frequency of nth cash flow (Fnn) 41
Frequency of X value (Ynn) 65
Future value (FV) 22, 23, 24
FV (future value) 22, 23, 24

G
Grouped cash flows 43

H
Hard reset 6
HYP (hyperbolic) indicator 3
Hyperbolic (HYP) indicator 3

I
I (discount rate) 41

106

I/Y (interest rate per year) 22, 24
Inflows 21, 23, 25
Initial cash flow (CFo) 41
INS (insert) indicator 3
Insert (IND) indicator 3
INT (interest paid) 22, 24
Interest Conversion worksheet 73
Interest paid (INT) 22, 24
Interest rate per year (I/Y) 22, 24
Internal rate of return (IRR) 41, 45
INV (inverse) indicator 3
Inverse (INV) indicator 3
IRR (internal rate of return) 41, 45

L
Last Answer (ANS) feature 14
Leases 21
LIF (life of the asset) 57, 59, 60
Life of the asset (LIF) 57, 59, 60
LIN (linear regression) 63, 65
Linear regression (LIN) 63, 65
Ln (logarithmic regression) 63, 65
Loans 21, 24
Logarithmic regression (Ln) 63, 65

M
M01 (starting month) 57, 59, 60
M0–M9 (memory) 12, 80, 81
MAR (profit margin) 77, 78
Math operations 8
Mean of X (() 63, 65
Mean of Y (() 63
Memory
arithmetic 12
clearing 12
examples 12
recalling from 12
storing to 12
Memory worksheet 80–81
MOD (modified internal rate of
return) 41
Modified duration (DUR) 52
Modified internal rate of return
(MOD) 41
Mortgages 21
Multiplication 8

Index

N
n (number of observations) 63, 65
N (number of periods, TVM
worksheet) 22
N (number of periods) 24
Negative (–) indicator 3
Net present value (NPV) 41, 44
NEW (new value) 70, 71, 72
New value (NEW) 70, 71, 72
NOM (nominal rate) 74
Nominal rate (NOM) 74
NPV (net present value) 41, 44
Number of observations (n) 63, 65
Number of periods (#PD) 70, 71, 72
Number of periods (#PD), Percent
Change/Compound Interest
worksheet 70
Number of periods (N) 24
Number of periods (N), TVM
worksheet 22
Number separators format 4

O
OLD (old value) 70, 71, 72
Old value (OLD) 70, 71, 72
One coupon per year (1/Y) 52, 53, 55
One-variable statistics (1-V) 63, 65
Outflows 21, 25
Overview of calculator operation 1–
19

P
P (unit price) 79
P/Y (payments per year) 22, 24, 25
P1 (starting payment) 22, 24
P2 (ending payment) 22, 24
Par value 54
Parentheses 8, 10
Payment (PMT) 22, 23, 24
Payments per year (P/Y) 22, 24, 25
Percent 8
Percent add-on 8
Percent change (%CH) 70, 71, 72
Percent Change/Compound Interest
worksheet 69
Percent discount 8

Index

Percent ratio 8
Permutations 8, 10
PFT (profit) 79
PMT (payment) 22, 23, 24
Population standard deviation of X
((x) 63, 65
Population standard deviation of Y
((y) 63
Power regression (PWR) 63, 65
Predicted X value (X') 63, 65, 67
Predicted Y value (Y') 63, 65, 67
Premium bond 54
Present value (PV) 22, 23, 24
PRI (bond price) 56
PRI (dollar price) 52, 54, 55
Principal paid (PRN) 22, 24
PRN (principal paid) 22, 24
Procedures
computing accrued interest 55
computing basic loan interest 26
computing bond price 55
computing bond yield 55
computing breakeven 79
computing breakeven quantity
79
computing compound interest
70
computing cost-sell-markup 70
computing dates 76
computing internal rate of
return 45
computing net present value 45
computing percent change 70
computing profit margin 78
computing statistical results 66,
67
computing X’ 67
computing Y’ 67
constants for various operations
13
converting interest 74
deleting cash flows 43
entering bond data 55
entering cash flows 43
entering data points 66
entering depreciation data 60
generating a depreciation
schedule 60
107

Q

bond variables 52
breakeven variables 79
cash flow variables 42
date variables 75
depreciation variables 58
interest conversion variables 73
percent change/compound
interest variables 70
statistics variables 64
TVM variables 23
Resetting calculator 6
hard reset 6
pressing keys 6
RI (reinvestment rate) 41
Rounding 10, 94
RV (redemption value) 52, 53, 54, 55

Q (quantity) 79
Quantity (Q) 79

S

generating amortization
schedules 25, 26
inserting cash flows 44
selecting a depreciation method
60
selecting a statistics calculation
method 66, 67
selecting bond settings 55
using the memory worksheet 81
Profit (PFT) 79
Profit margin (MAR) 77, 78
Profit Margin worksheet 77–78
PV (present value) 22, 23, 24
PWR (power regression) 63, 65

R
r (correlation coefficient) 63, 66
RAD (radians) 5
RAD (radians) indicator 3
Radians (RAD) 5
Radians (RAD) indicator 3
Random numbers 10
RBV (remaining book value) 57, 58,
60
RDT (redemption date) 52, 53, 54, 55
RDV (remaining depreciable value)
57, 58, 60
Reading the display 2
Recalling from memory 12
Redemption date (RDT) 52, 53, 54, 55
Redemption value (RV) 52, 53, 54
Regression models
exponential 65
linear 65
logarithmic 65
power 65
Reinvestment rate (RI) 41
Remaining book value (RBV) 57, 58,
60
Remaining depreciable value (RDV)
57, 58, 60
Resetting
amortization variables 23
108

SAL (salvage value) 57, 60
Salvage value (SAL) 57, 60
Sample standard deviation of X (Sx)
63, 65
Sample standard deviation of Y (Sy)
63
Savings 21
Schedule 25
Scientific notation 11
SDT (settlement date) 52, 54, 55
Second (2nd)
functions 2
indicator 3
Quit 2
SEL (selling price) 77, 78
Selling price (SEL) 77, 78
service and support 98
SET (setting) indicator 3
Setting (SET) indicator 3
Settlement date (SDT) 52, 54, 55
SL (straight line) 57, 59, 60
SLF (French straight line) 57, 59, 60
Slope (b) 63
Square 8
Square root 8
Starting date (DT1) 60
Starting month (M01) 57, 59, 60
Starting payment (P1) 22, 24
Statistical data 66

Index

Statistics worksheet 63–67
Storing to memory 12
Straight line (SL) 57, 59, 60
Subtraction 8
Sum of the years’ digits (SYD) 57, 59,
60
Sum of X ((X) 63, 65
Sum of X2 ((X2) 63, 65
Sum of XY products ((XY) 63
Sum of Y ((Y) 63
Sum of Y2 ((Y2) 63
support and service 98
Sx (sample standard deviation of X)
63, 65
Sy (sample standard deviation of Y)
63
SYD (sum of the years’ digits) 57, 59,
60

T
Time-Value-of-Money (TVM)
worksheet 15, 16, 18, 21
Time-Value-of-Money and
Amortozation worksheets ??–40
Turning calculator off 1
Turning calculator on 1
TVM (Time-Value-of-Money)
worksheet 15, 16, 18, 21
Two coupons per year (2/Y) 52, 53, 55
Two-variable statistics 65, 67

U
Uneven cash flows 42
Unit price (P) 79
Universal power 8

V
Value assigned (=) indicator 3
Value computed (*) indicator 3
Value entered (Ä) indicator 3

Index

Variable cost per unit (VC) 79
VC (variable cost per unit) 79

W
What-if calculations 15
Worksheets
Amortization 21
Bond 51
Breakeven 78
Cash Flow 41
Date 75
Depreciation 57
display indicators 19
Interest Conversion 73
Memory 80
Percent Change/Compound
Interest 69
Profit Margin 77
prompted 18
TVM (Time-Value-of-Money) 15,
16, 18, 21
variables 15, 16, 17, 18

X
X value (Xnn) 63, 65
X' (predicted X value) 63, 65, 67
Xnn (X value) 63, 65
xP/Y key (multiply payments per
year) 25

Y
Y' (predicted Y value) 63, 65
Year to compute (YR) 57, 59, 60
Yield to maturity 54
Yield to redemption (YLD) 52, 55
Y-intercept (a) 63
YLD (yield to redemption) 52, 55
Ynn (frequency of X value) 63, 65
YR (year to compute) 57, 59, 60

109

110

Index



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