Select Page

# Present Value of Annuity Problems and Solutions

## Problem 1:

You are making car payments of \$315/month for the next 3 years, you know that your car loan has an interest rate of 12.4%, discounted monthly, what was the initial price of the car?

## Problem 2:

Mr. Naeem has won a scholarship which pays him \$5,000 per year for 3 years beginning a year from today. He wants to know the present value of the scholarship using a discount rate of 7%. Solve by Factor Formula?

### Solution:

PVA3 = 5,000 (PVIFA 7%, 3)

PVA3 = 5,000 (2.6243)

## Problem 3:

What is the present value of an annuity of \$2,000 per year, with the first cash flow received three years from today and the last one received 8 years from today?  Use a discount rate of eight percent.

### Solution:

PVA6 = \$9,245.76

PV2 = 9,245.76 / (1 + 0.08) 2

## Problem 4:

Find the present value of an annuity with periodic payments of \$2,000, for a period of 10 years at an interest rate of 6%, discounted semiannually by factor formula?

### Solution:

PVA10 = 2,000 (PVIFA 6%/2, 10*2)

PVA10 = 2,000 (2.1065)

## Problem 5:

Mr. Mohammad Ali has received a job offer from a large investment bank as an accountant.  His base salary will be \$35,000 constant to date of retirement.  He will receive his first annual salary payment one year from the day he begins to work.  In addition, he will get an immediate \$10,000 bonus for joining the company.   Mr. Ali is expected to work for 25 years. What is the present value of the offer if the discount rate is 12 percent?

### Solution:

PVA25 = 274,509.87

Bonus = 10,000

## Problem 6:

Mr. Khaild will receive \$8,500 a year for the next 15 years from her trust.  If a 7 percent interest rate is applied, what is the current value of the future payments if first receipt occurs today?

## Problem 7:

What is the present value of an annuity due that makes 5 annual payments of \$200 each if the discount rate is 12% by general formula constant rate and general floating formula?

## Problem 8:

A 10-year annuity pays \$900 four times in year.  The first \$900 will be paid five years from now.  If the stated interest rate is eight percent, discounted quarterly, what is the present value of this annuity?

### Solution:

PVA6 = \$17,022.53

PV4 = 17,022.53/ (1 + 0.08/4) 4*4

## Problem 9:

Find the present value of due annuity with periodic payments of \$2,000, for a period of 10 years at an interest rate of 6%, discounted semiannually by factor formula and table.

### Solution:

2,000 (PVIFA 6%/2, 10*2)

2,000 (14.877)

## Problem 10:

You have won the lottery!  The lottery officials offer you two choices for collecting your winnings.  You may take four payments of \$250,000 over the next four years or, you may take a one-time payment of \$750,000 today.  Which would you take?