Calculator, HP 10 BII, Annuity

Finance Calculator
HP 10BII

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: Orange key, C ALL
Step 2: Proper compounding: press 1, the yellow button, and then P/YR (which is on the first row fourth column below the PMT key).

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: Orange key, C ALL
Step 2: Change the compounding: 12, orange key, P/YR (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: Orange key, C 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: Orange key, C ALL
Step 2: Change the compounding: 12, orange key, P/YR (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: Orange key, C 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)

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: Orange key, C 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

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: Orange key, C 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

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.

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:
Orange key, BEG/END, (second row first column from the right). The BEGIN announciator is displayed when your calculator is in Begin mode.

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: Orange key, C ALL
Step 2: Proper compounding: press 1, the yellow button, and then P/YR (which is on the first row fourth column above the PMT key).

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

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: Orange key, C 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

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: Orange key, C 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

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: Orange key, C 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+/-

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: Orange key, C 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

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

Last Updated on 1 May 2002, e-mail any comments to: robert.balik@wmich.edu