Finance
Calculator
Texas Instruments BA II +
Annuities. Time Value of Money Problems using multiple
payments of equal value
a. Future Value of a Regular Annuity
What is the Future Value of 10 equal end of period payments of $100 each,
invested at an annual interest rate of 10 percent
Note:
All the Time Value of Money keys are on the third row of the calculator.
Always press the number first before pressing the Time Value of Money Keys.
Clear time value of money memory: 2nd CLR TVM (above the FV
key)
Compounding should remain at P/Y = 1 (third row second column), ENTER
(first row second column), down arrow (first row fourth column), C/Y
= 1.
Enter number of years: N = 10
Enter interest rate: i = 10 (press 10 and then I/Y)
Enter payment: PMT = 100 +/- (press 100,+/-, so it looks
like -100, and then PMT)
Not using Present Value key: PV = 0
Calculate unknown: CPT FV, answer is $1,593.742 (CPT can
be found on the first row first column)
Another way of doing this problem,
Clear time value of money memory: 2nd CLR TVM (above the FV
key)
Change the compounding: 2nd, P/Y=12 (third row second column), ENTER
(first row second column),
down arrow (first row fourth column), C/Y = 12. This is
to change from monthly payment to annually payment.
Enter number of years: N = 10
Enter interest rate: i = 120 (press 120 and then I/Y)
Enter payment: PMT = 100 +/- (press 100,+/-, so it looks
like -100, and then PMT)
Not using Present Value key: PV = 0
Calculate unknown: CPT FV, answer is $1,593.742 (CPT can
be found on the first row first column)
b. Unkown: Number of years.
$1,593.74 is needed sometime in the future. How long, investing $100 per year, earning
10 percent annually, would it take to amass this amount of money?
Clear time value of money memory: 2nd CLR TVM
Compounding should remain at P/Y = 1 and C/Y = 1
Enter interest rate: i = 10
Enter payment: PMT = 100
Enter Future Value: FV = 1593.74+/-
Not using Present Value key: PV = 0
Calculate unknown: CPT N, answer is 9.999 (round to 10)
Another way of doing this problem,
Clear time value of money memory: 2nd CLR TVM (above the FV
key)
Change the compounding: 2nd, P/Y=12 (third row second column), ENTER
(first row second column),
down arrow (first row fourth column), C/Y = 12. This is
to change from monthly payment to annually payment.
Enter interest rate: i = 120
Enter payment: PMT = 100
Enter Future Value: FV = 1593.74+/-
Not using Present Value key: PV = 0
Calculate unknown: CPT N, answer is 9.999 (round to 10)
c. Unkown: Interest rate needed
Once again, $1,593.74 is needed, and you know ahead of time that you have
10 years to obtain it. What annual interest rate would a $100 annuity have to earn for you
to achieve this goal?
Clear time value of money memory: 2nd CLR TVM
Compounding should remain at P/Y = 1 and C/Y = 1
Enter payment: PMT = 100
Enter Future Value: FV = 1593.74+/-
Enter Present Value: PV = 0
Enter number of years: N = 10
Calculate unknown: CPT i (I/Y), answer is 9.999 (round
to 10)
Another way of doing this problem,
Clear time value of money memory: 2nd CLR TVM (above the FV
key)
Change the compounding: 2nd, P/Y=12 (third row second column), ENTER
(first row second column),
down arrow (first row fourth column), C/Y = 12. This is
to change from monthly payment to annually payment.
Enter payment: PMT = 100
Enter Future Value: FV = 1593.74+/-
Enter Present Value: PV = 0
Enter number of years: N = 10
Calculate unknown: CPT i (I/Y), answer is 120. But,
since this is the annual payment, divide the result by12, therefore the answer is 9.999
(round to 10)
d. Unknown: Payment.
To obtain an amount of $2000.00 ten years from now, earning 10 percent annually, what
amount would have to be invested on a yearly basis?
Clear time value of money memory: 2nd CLR TVM
Compounding should remain at P/Y = 1 and C/Y = 1
Enter Future Value: FV = 2000.00+/-
Enter Present Value: PV = 0
Enter number of years: N = 10
Enter interest rate: i = 10
Calculate unknown: CPT PMT, answer is $125.49
Another way of doing this problem,
Clear time value of money memory: 2nd CLR TVM (above the FV
key)
Change the compounding: 2nd, P/Y=12 (third row second column), ENTER
(first row second column),
down arrow (first row fourth column), C/Y = 12. This is
to change from monthly payment to annually payment.
nter Future Value: FV = 2000.00+/-
Enter Present Value: PV = 0
Enter number of years: N = 10
Enter interest rate: i = 120
Calculate unknown: CPT PMT, answer is $125.49
e. Present Value of a Regular Annuity
What is the present value of a 4 year annuity, with payments of $100
earning 10 percent annually?
Clear time value of money memory: 2nd CLR TVM
Compounding should remain at P/Y = 1 and C/Y = 1
Enter number of years: N = 4
Enter Interest Rate: i = 10
Enter Payments: PMT = $100+/-
Enter Future Value: FV = 0
Calculate unknown: CPT PV,
answer is $316.99
Another way of doing this problem,
Clear time value of money memory: 2nd CLR TVM (above the FV
key)
Change the compounding: 2nd, P/Y=12 (third row second column), ENTER
(first row second column),
down arrow (first row fourth column), C/Y = 12. This is
to change from monthly payment to annually payment.
Enter number of years: N
= 4
Enter Interest Rate: i = 120
Enter Payments: PMT = $100+/-
Enter Future Value: FV = 0
Calculate unknown: CPT PV,
answer is $316.99
*** The previous problems all deal
with a regular annuities. The next set deals with an annuity due. The difference being
that with an annuity due, payments are made at the beginning of the compounding periods.
Annuities Due: Time Value of Money Problems using
equal beginning of period payments.
To change the setting on the calculator from regular to annuity due:
2nd BGN (third row above PMT key), 2nd SET
(first row second column above ENTER key), after these 2 steps BGN should appear in the
upper right corner of display.
a. Unknown: FV or Future Value.
What is the Future Value of ten equal beginning of period payments of $100 each,
invested at an annual interest rate of 10 percent.
Clear time value of money memory: 2nd CLR TVM (above the FV
key)
Compounding should remain at P/Y = 1 (third row second column), ENTER
(first row second column), down arrow (first row fourth column), C/Y
= 1.
Enter number of years: N = 10
Enter interest rate: i = 10 (press 10 and then I/Y)
Enter amount of payments: PMT = 100 +/- (press 100,+/-,
so it looks like -100 and then PMT)
Enter Present Value: PV = 0
Calculate unknown: CPT FV, answer is $1,753.12 (CPT
can be found on first row first column)
Another way of doing this problem,
Clear time value of money memory: 2nd CLR TVM (above the FV
key)
Change the compounding: 2nd, P/Y=12 (third row second column), ENTER
(first row second column),
down arrow (first row fourth column), C/Y = 12. This is
to change from monthly payment to annually payment.
Enter number of years: N = 10
Enter interest rate: i = 10 (press 10 and then I/Y)
Enter amount of payments: PMT = 100 +/- (press 100,+/-,
so it looks like -100 and then PMT)
Enter Present Value: PV = 0
Calculate unknown: CPT FV, answer is $1,753.12 (CPT
can be found on first row first column)
b. Unknown: Number of years
$1,753.12 is needed sometime in the future. How long, investing $100 per
year, earning 10 percent annually, would it take to amass this amount of money?
Clear time value of money memory: 2nd CLR TVM
Compounding should remain at P/Y = 1 and C/Y = 1
Enter interest rate: i = 10
Enter payment: PMT = 100
Enter Future Value: FV = 1753.12+/-
Not using Present Value key: PV = 0
Calculate unknown: CPT N, answer is 10
Another way of doing this problem,
Clear time value of money memory: 2nd CLR TVM (above the FV
key)
Change the compounding: 2nd, P/Y=12 (third row second column), ENTER
(first row second column),
down arrow (first row fourth column), C/Y = 12. This is
to change from monthly payment to annually payment.
Enter interest rate: i = 120
Enter payment: PMT = 100
Enter Future Value: FV = 1753.12+/-
Not using Present Value key: PV = 0
Calculate unknown: CPT N, answer is 10
c. Unkown: Interest rate needed
This time $1,500 is needed, and you know in advance that you have 10 years
to obtain it. What annual interest rate would a $100 annuity due have to earn for you to
achieve this goal?
Clear time value of money memory: 2nd CLR TVM
Compounding should remain at P/Y = 1 and C/Y = 1
Enter payment: PMT = 100
Enter Future Value: FV = 1500.00+/-
Enter Present Value: PV = 0
Enter number of years: N = 10
Calculate unknown: CPT i (I/Y), answer is 7.26 percent
Another way of doing this problem,
Clear time value of money memory: 2nd CLR TVM (above the FV
key)
Change the compounding: 2nd, P/Y=12 (third row second column), ENTER
(first row second column),
down arrow (first row fourth column), C/Y = 12. This is
to change from monthly payment to annually payment.
Enter payment: PMT = 100
Enter Future Value: FV = 1500.00+/-
Enter Present Value: PV = 0
Enter number of years: N = 10
Calculate unknown: CPT i (I/Y), answer is 87.08 percent.
But, since this is the annual payment, divide the result by 12 to get the monthly rate.
The answer is 7.26 percent.
d. Unknown: Payment
To obtain an amount of $3000.00 ten years from now, earning 10 percent
annually, what amount would have to be invested on a yearly basis in an annuity due form?
Clear time value of money memory: 2nd CLR TVM
(above the FV key)
Compounding should remain at P/Y = 1 and C/Y = 1
Enter Future Value: FV = 3000.00+/-
Enter Present Value: PV = 0
Enter number of years: N = 10
Enter interest rate: i = 10
Calculate unknown: CPT PMT, answer is $171.12
Another way of doing this problem,
Clear time value of money memory: 2nd CLR TVM (above the FV
key)
Change the compounding: 2nd, P/Y=12 (third row second column), ENTER
(first row second column),
down arrow (first row fourth column), C/Y = 12. This is
to change from monthly payment to annually payment.
Enter Future Value: FV = 3000.00+/-
Enter Present Value: PV = 0
Enter number of years: N = 10
Enter interest rate: i = 120
Calculate unknown: CPT PMT, answer is $171.12
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Last Updated on 1 May 2002, e-mail any comments to: robert.balik@wmich.edu |