Texas Instruments BA II Plus Manuale utente

April 2007

GENERAL INFORMATION

The Texas Instrument BA II Plus financial calculator was designed to support the many possible

applications in the areas of financial analysis and banking.

The explanations below will make it easier for you to use the calculator.

By default, the calculator operates in financial mode.

The ON/OFF key is used to turn the calculator on and off.

The 2ND key is often used to access financial applications. Press this key when you

want to apply the functions displayed in yellow at the top of the keys.

The FORMAT feature lets you select the number of decimal points to be displayed by the

calculator. If you want to display:

¾a fixed decimal point, press 2ND and then FORMAT, enter a number from 0 to 8

to specify the number of decimal points, and then press ENTER.

¾a floating decimal point, press 2ND and then FORMAT, enter the number 9, and

then press ENTER. The number of decimals displayed will vary depending on the

calculations up to a maximum of nine decimals.

To perform the calculator exercises in this document, it is best to use a floating decimal

point format.

Setting the number of payment periods and interest-calculation periods in a financial

calculation (the P/Y and C/Y functions).

¾P/Y function: this function sets the number of annual payments. The default value

is one payment per year. To change the number of annual payments, press the

2ND and P/Y keys, enter the required value, and then press ENTER (for

example, 12 for 12 monthly payments).

¾C/Y function: this function sets the number of interest-calculation periods. By

default, the number of interest-calculation periods is the same as the number

entered for the P/Y variable. To change it, press 2ND, P/Y and È, and then enter

the number of periods and press ENTER.

Example where the C/Y differs from the P/Y: monthly payments on a personal loan on

which interest is calculated quarterly (I, 4):

Sequence of entries Display Explanation

2ND >P/Y >12 >ENTER P/Y = 12 Enters a monthly payment

period (12 months).

2ND >P/Y >È> 4 >

ENTER C/Y = 4 Enters a quarterly interest-

calculation period (4 three-

month periods per year).

N. B.: It is important to follow the sequence of entries without pressing any other key.

The BGN function lets you activate the beginning-of-period or the end-of-period payment.

To understand the configuration of this function, simply press the 2ND and BGN keys. To

the left of your screen, you will then see the END or BGN letters.

To activate the beginning-of-period payment calculation, simply press the 2ND, BGN,

2ND and SET keys. The BGN indicator then appears in the upper-right area of the

display screen. To return to END, simply repeat the 2ND, BGN, 2ND and SET sequence:

the BGN indicator will disappear.

The CE/C key clears the on-screen data without deleting any numerical values that have

been entered.

The CLR TVM function cancels the numeric values and calculation commands and

resets the calculator’s default financial values. Before performing each calculation, users

are advised to cancel all previously used numerical values by pressing the 2ND and CLR

TVM keys.

These keys, however, do not affect the beginning-of-year payment (BGN) mode or end-

of-period payment (END) mode or the values attributed to P/Y and C/Y. Therefore, it is

important to make sure that these values have been programmed before performing a

calculation.

FINANCIAL CALCULATIONS

Most financial calculations are carried out using the following seven keys:

Financial keys These keys are used to designate or calculate:

N The number of periods.

I/Y The nominal interest rate.

PV The present value of an investment.

FV The future value of an investment.

PMT The periodic payment of an amortized loan or a split

annuity.

CPT Compute key.

BGN Indicates whether the calculations include the payments

made at the beginning or at the end of each period.

Note:

By convention, the present value of an investment is a negative value. The calculator is

programmed this way; therefore, in calculations of future values or per-period payments, if the

present value is entered as a negative value, the future value or the value of the payments will

be positive. The opposite is also true. It is therefore important to be thorough and refer to the

calculator’s user guide, if necessary.

Sample calculation of the future value (FV) of a single payment

Someone wishes to invest $4,000 in a registered retirement savings plan (RRSP) for a five-year

period.

Insurer A proposes an annual compound interest rate of 6%, whereas insurer B proposes a

nominal rate of 5.95% compounded on a semi-annual basis. The following two tables should

help you determine which insurer is proposing the best investment.

Insurer A

Sequence of entries Display Explanation

CE/C > 2ND > CLR TVM 0 Resets the default values.

2ND > P/Y > 1 > ENTER P/Y = 1 Enters an annual payment period.

CE/C > CE/C 0 Exits the entry of the P/Y variable.

5 > N N = 5 Enters a five-year period.

6 > I/Y I/Y = 6 Enters an annual interest rate of 6%.

4,000 > +/−> PV PV = −4,000 Enters the present value of the

investment.

CPT > FV FV = 5,352.90231 Calculates the final value of the

investment.

Insurer B

Sequence of entries Display Explanation

CE/C > 2ND > CLR TVM 0 Resets the default values.

2ND > P/Y > 2 > ENTER P/Y = 2 Enters a semi-annual payment period.

CE/C > CE/C 0 Exits the entry of the P/Y variable.

5 > 2ND > xP/Y > N N = 10 Enters the number of periods over five

years.

5.95 > I/Y I/Y = 5.95 Enters a nominal interest rate of 5.95%.

4,000 > +/−> PV PV = −4,000 Enters the present value of the investment.

CPT > FV FV = 5,362.632027 Calculates the final value of the

investment.

The investment proposed by Insurer B returns a greater cumulative value, after five years, of

approximately $9.73.

Calculating the future value of an annuity

A client would like to invest $2,500 per year over the next five years. He would like to know what

the cumulative value of the investment would be in five years if the annual realized rate were 5%

in a situation where the investment is made at the beginning of the year and in a situation where

the investment is made at the end of the year.

¾$2,500 investment made at the beginning of the year

Sequence of entries Display Explanation

CE/C > 2ND > CLR TVM 0 Resets the default values.

2ND > BGN > 2ND >

SET BGN Activates the calculation of beginning-of-

period payments.

2ND > P/Y > 1 > ENTER P/Y = 1 Enters an annual payment period.

CE/C > CE/C 0 Exits the entry of the P/Y variable.

2,500 > +/−> PMT PMT = −2,500 Enters the amount of the annual

investment.

5 > N N = 5 Enters the number of periods.

5 > I/Y I/Y = 5 Enters the annual interest rate.

CPT > FV FV = 14,504.78203 Calculates the cumulative value of the

annuity.

¾$2,500 investment made at the end of the year

Sequence of entries Display Explanation

CE/C > 2ND > CLR TVM 0 Resets the default values.

2ND > BGN > 2nd > SET END Activates the calculation of end-of-period

payments.

2ND > P/Y > 1 > ENTER P/Y = 1 Enters an annual payment period.

CE/C > CE/C 0 Exits the entry of the P/Y variable.

2,500 > +/−> PMT PMT = −2,500 Enters the amount of the annual

investment.

5 > N N = 5 Enters the number of periods.

5 > I/Y I/Y = 5 Enters the annual interest rate.

CPT> FV FV = 13,814.07812 Calculates the cumulative value of the

annuity.

Obviously, an investment made at the beginning of the year will result in a higher cumulative

value (other variables being equal), as the interest will begin to accumulate on the very first day.

Calculating the payment of a personal or mortgage loan

The process of calculating a personal or mortgage loan consists of:

Determining the known variables;

Entering the number of payment periods (P/Y) and the number of interest-calculation

periods (C/Y);

Calculating the unknown variable.

Sample calculation of a personal loan repayment

Mary wants to borrow $15,000 to purchase a new car, and she wants to repay the loan over a

five-year period. If the bank demands a nominal rate of 6% compounded on a monthly basis,

what would be the monthly repayment (end of period)?

Known variables:

- nominal rate: (6%,12)

- term of the loan: five years (60 monthly payments)

- capital borrowed: $15,000

- Number of annual payments: 12

- Number of interest-calculation periods: 12

The monthly repayment can be calculated using the following operations:

Sequence of entries Display Explanation

CE/C > 2ND > CLR TVM 0 Resets the default values.

2ND > P/Y > 12 > ENTER P/Y = 12 Enters a monthly payment period.

CE/C > CE/C 0 Exits the entry of the P/Y variable.

5 > 2ND > xP/Y > N N = 60 Enters the number of monthly payments

over five years.

6 > I/Y I/Y = 6 Enters the nominal interest rate.

15,000 > +/−> PV PV = −15,000 Enters the amount of the loan.

CPT > PMT PMT = 289.9920229 Calculates the amount of the monthly

payments.

To repay this loan over a five-year period, the monthly repayment amount would be $289.99.

Sample calculation of a mortgage loan repayment

Claude buys a home for $125,000 and makes a $40,000 cash downpayment. To finance the

balance, the bank offers him an $85,000 mortgage loan at a nominal rate of 6% compounded on

a semi-annual basis.

What monthly payments will be required to repay this mortgage over a 20-year term?

What will the mortgage balance be after five years?

To answer these two questions, the known variables must first be determined:

- nominal rate: (6%, 2)

- term of the loan: 20 years (240 monthly payments)

- capital borrowed: $85,000

The monthly mortgage repayment can be calculated using the following operations:

Sequence of entries Display Explanation

CE/C > 2ND > CLR

TVM 0 Resets the default values.

2ND > P/Y > 12 >

ENTER P/Y = 12 Enters a monthly payment period.

È> 2 > ENTER C/Y = 2 Enters a semi-annual interest-

calculation period.

CE/C > CE/C 0 Exits the entry of the C/Y variable.

20 > 2ND > xP/Y > N N = 240 Enters the number of monthly

payments over a 20-year period.

6 > I/Y I/Y = 6 Enters the nominal interest rate.

85,000 > +/−> PV PV = −85,000 Enters the loan amount.

CPT > PMT PMT = 605.3601756 Calculates the monthly repayment

amount.

To repay this loan over a 20-year period, the monthly repayment amount would be $605.36.

The balance of the mortgage loan after five years is calculated using the following operations,

after having computed the monthly payment of $605.36:

Sequence of entries Display Explanation

Do not change the data already entered for the financial variables

5 > 2ND > xP/Y > N N = 60 Enters the number of monthly

payments over a five-year period.

CPT > FV FV = 72,076,74454 Calculates the loan balance after 60

monthly payments.

The balance of the mortgage loan after five years is therefore $72,076.74.

In financial mathematics, it is often a good idea to double-check calculations. In this example,

another way to calculate the mortgage balance after 5 years would be to calculate the

present value of monthly payments of $605.36 over 15 years, i.e., the remaining term of the

loan.

The balance of the mortgage loan after five years can be calculated using the following

operations:

Sequence of entries Display Explanation

CE/C > 2ND > CLR TVM 0 Resets the default values.

2ND > P/Y > 12 >

ENTER P/Y = 12 Enters a monthly payment period.

È> 2 > ENTER C/Y = 2 Enters a semi-annual interest-

calculation period.

CE/C > CE/C 0 Exits the entry of the C/Y variable.

15 > 2ND > xP/Y > N N = 180 Enters the number of monthly

payments for the 15 remaining

years.

6 > I/Y I/Y = 6 Enters the nominal interest rate.

605.3601756 > PMT PMT = 605.3601756 Enters the amount of the monthly

payments.

CPT > PV PV = −72,076.74454 Calculates the loan balance after 60

monthly payments.

The balance of the mortgage loan after five years is therefore $72,076.74.

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