Finance
Calculator
HP 10B
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 first row of the calculator.
Always press the number first before pressing the Time Value of Money Keys.
Step 1: Clear time value of money memory: 2nd CLEAR
ALL (third row above the INPUT KEY)
Step 2: Proper compounding: press 1, the yellow
button (work as 2nd shift key), and then P/YR (which is on the
first row fourth column above the PMT key). To check, press the yellow button
and then INPUT. (you should be able to see 1_P_Yr)
Step 3 (Calculation):
Enter number of years: N = 10 (press 10 and then N)
Enter interest rate: i(I/YR) = 10 (press 10 and then
I/Y)
Enter payment: PMT = -100 (press 100, +/-, and then PMT)
Not using Present Value key: PV = 0 (press 0 and then PV)
Calculate unknown: Press FV, answer is $1,593.742
Another way of doing this problem,
Step 1: Clear time value of money memory: 2nd CLEAR
ALL (above the INPUT key)
Step 2: Change the compounding: 2nd, P/YR = 12 (first
row fourth column). This is to change from monthly payment to annually
payment.
Step 3 (Calculation):
Enter number of years: N = 10 (press 10 and then N)
Enter interest rate: i(I/YR) = 120 (press 120 and then
I/Y)
Enter payment: PMT = -100 (press 100, +/-, and then PMT)
Not using Present Value key: PV = 0 (press 0 and then PV)
Calculate unknown: Press FV, answer is $1,593.742
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?
Step 1: Clear time value of money memory: 2nd CLEAR
ALL
Step 2: Compounding should remain at P/Y = 1 and C/Y = 1
Step 3 (Calculation):
Enter interest rate: i = 10
Enter payment: PMT = 100
Enter Future Value: FV = 1593.74+/-
Not using Present Value key: PV = 0
Calculate unknown: Press N, answer is 9.999 (round to 10)
Another way of doing this problem,
Step 1: Clear time value of money memory: 2nd CLEAR
ALL (above the INPUT key)
Step 2: Change the compounding: 2nd, P/YR = 12 (first
row fourth column). This is to change from monthly payment to annually
payment.
Step 3 (Calculation):
Enter interest rate: i = 120
Enter payment: PMT = 100
Enter Future Value: FV = 1593.74+/-
Not using Present Value key: PV = 0
Calculate unknown: Press 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?
Step 1: Clear time value of money memory: 2nd CLEAR
ALL
Step 2: Compounding should remain at P/Y = 1 and C/Y = 1
Step 3 (Calculation):
Enter payment: PMT = 100
Enter Future Value: FV = 1593.74+/-
Enter Present Value: PV = 0
Enter number of years: N = 10
Calculate unknown: Press i(I/YR), answer is 9.999 (round to 10)
Another way of doing this problem,
Step 1: Clear time value of money memory: 2nd CLEAR
ALL (above the INPUT key)
Step 2: Change the compounding: 2nd, P/YR = 12 (first
row fourth column). This is to change from monthly payment to annually
payment.
Step 3 (Calculation):
Enter payment: PMT = 100
Enter Future Value: FV = 1593.74+/-
Enter Present Value: PV = 0
Enter number of years: N = 10
Calculate unknown: Press i(I/YR), answer is 119.99 (round to 120)
But since this is the annual payment, divide the result by 12 to get the montly
payment of 10 percent.
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?
Step 1: Clear time value of money memory: 2nd CLEAR
ALL
Step 2: Compounding should remain at P/Y = 1 and C/Y = 1
Step 3 (Calculation):
Enter Future Value: FV = 2000.00+/-
Enter Present Value: PV = 0
Enter number of years: N = 10
Enter interest rate: i = 10
Calculate unknown: Press PMT, answer is $125.49
Another way of doing this problem,
Step 1: Clear time value of money memory: 2nd CLEAR
ALL (above the INPUT key)
Step 2: Change the compounding: 2nd, P/YR = 12 (first
row fourth column). This is to change from monthly payment to annually
payment.
Step 3 (Calculation):
Enter Future Value: FV = 2000.00+/-
Enter Present Value: PV = 0
Enter number of years: N = 10
Enter interest rate: i = 120
Calculate unknown: Press 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?
Step 1: Clear time value of money memory: 2nd
CLEAR ALL
Step 2: Compounding should remain at P/Y = 1 and C/Y = 1
Step 3 (Calculation):
Enter number of years: N = 4
Enter Interest Rate: i = 10
Enter Payments: PMT = $100+/-
Enter Future Value: FV = 0
Calculate unknown: Press PV,
answer is $316.99
Another way of doing this problem,
Step 1: Clear time value of money memory: 2nd CLEAR
ALL (above the INPUT key)
Step 2: Change the compounding: 2nd, P/YR = 12 (first
row fourth column). This is to change from monthly payment to annually
payment.
Step 3 (Calculation):
Enter number of years: N = 4
Enter Interest Rate: i = 120
Enter Payments: PMT = $100+/-
Enter Future Value: FV = 0
Calculate unknown: Press 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.
IV. 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, (BGN should appear in the last row second column above 0)
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.
Note:
All the Time Value of Money keys are on the first row of the calculator.
Always press the number first before pressing the Time Value of Money Keys.
Step 1: Clear time value of money memory: 2nd CLEAR
ALL (third row above the INPUT KEY)
Step 2: Proper compounding: press 1, the yellow
button (work as 2nd shift key), and then P/YR (which is on the
first row fourth column above the PMT key). To check, press the yellow button
and then INPUT. (you should be able to see 1_P_Yr)
Step 3 (Calculation):
Enter number of years: N = 10
Enter interest rate: i(I/YR) = 10
Enter amount of payments: PMT = 100+/-
Enter Present Value: PV = 0
Calculate unknown: Press FV, answer is $1,753.12
Another way of doing this problem,
Step 1: Clear time value of money memory: 2nd CLEAR
ALL (above the INPUT key)
Step 2: Change the compounding: 2nd, P/YR = 12 (first
row fourth column). This is to change from monthly payment to annually
payment.
Step 3 (Calculation):
Enter number of years: N = 10
Enter interest rate: i(I/YR) = 120
Enter amount of payments: PMT = 100+/-
Enter Present Value: PV = 0
Calculate unknown: Press FV, answer is $1,753.12
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?
Step 1: Clear time value of money memory: 2nd CLEAR
ALL
Step 2: Compounding should remain at P/Y = 1 and C/Y = 1
Step 3 (Calculation):
Enter interest rate: i = 10
Enter payment: PMT = 100+/-
Enter Future Value: FV = 1753.12
Not using Present Value key: PV = 0
Calculate unknown: Press N, answer is 10
Another way of doing this problem,
Step 1: Clear time value of money memory: 2nd CLEAR
ALL (above the INPUT key)
Step 2: Change the compounding: 2nd, P/YR = 12 (first
row fourth column). This is to change from monthly payment to annually
payment.
Step 3 (Calculation):
Enter interest rate: i = 120
Enter payment: PMT = 100+/-
Enter Future Value: FV = 1753.12
Not using Present Value key: PV = 0
Calculate unknown: Press 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?
Step 1: Clear time value of money memory: 2nd CLEAR
ALL
Step 2: Compounding should remain at P/Y = 1 and C/Y = 1
Step 3 (Calculation):
Enter payment: PMT = 100+/-
Enter Future Value: FV = 1500.00
Enter Present Value: PV = 0
Enter number of years: N = 10
Calculate unknown: PRESS i (I/YR), answer is 7.26 percent
Another way of doing this problem,
Step 1: Clear time value of money memory: 2nd CLEAR
ALL (above the INPUT key)
Step 2: Change the compounding: 2nd, P/YR = 12 (first
row fourth column). This is to change from monthly payment to annually
payment.
Step 3 (Calculation):
Enter payment: PMT = 100+/-
Enter Future Value: FV = 1500.00
Enter Present Value: PV = 0
Enter number of years: N = 10
Calculate unknown: PRESS i (I/YR), answer is 87.08 percent.
But since this is the annual payment, divide the result by 12 to get the montly payment of
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?
Step 1: Clear time value of money memory: 2nd CLEAR
ALL
Step 2: Compounding should remain at P/Y = 1 and C/Y = 1
Step 3 (Calculation):
Enter Future Value: FV = 3000.00
Enter Present Value: PV = 0
Enter number of years: n = 10
Enter interest rate: i = 10
Calculate unknown: PRESS PMT, answer is $171.12+/-
Another way of doing this problem,
Step 1: Clear time value of money memory: 2nd CLEAR
ALL (above the INPUT key)
Step 2: Change the compounding: 2nd, P/YR = 12 (first
row fourth column). This is to change from monthly payment to annually
payment.
Step 3 (Calculation):
Enter Future Value: FV = 3000.00
Enter Present Value: PV = 0
Enter number of years: n = 10
Enter interest rate: i = 120
Calculate unknown: PRESS PMT, answer is $171.12+/-
e. Present Value of an Annuity Due
What is the present value of a 4 year annuity due, with payments of $100 earning 10
percent annually?
Step 1: Clear time value of money memory: 2nd CLEAR
ALL
Step 2: Compounding should remain at P/Y = 1 and C/Y = 1
Step 3 (Calculation):
Enter number of years: N = 4
Enter Interest Rate: i = 10
Enter Payments: PMT = $100+/-
Enter Future Value: FV = 0
Calculate unknown: PRESS PV,
answer is $348.69
Another way of doing this problem,
Step 1: Clear time value of money memory: 2nd CLEAR
ALL (above the INPUT key)
Step 2: Change the compounding: 2nd, P/YR = 12 (first
row fourth column). This is to change from monthly payment to annually
payment.
Step 3 (Calculation):
Enter number of years: N = 4
Enter Interest Rate: i = 120
Enter Payments: PMT = $100+/-
Enter Future Value: FV = 0
Calculate unknown: PRESS PV,
answer is $385.60
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Last Updated on 1 May 2002, e-mail any comments to: robert.balik@wmich.edu |