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?

Solution: 

present value of annuity

Answer: $9,429.53

 

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)      

Answer: $13,121.5

>> Download Present Value of Annuity Table.

 

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: 

present value of an annuity

present value of annuity calculator

PVA6 = $9,245.76

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

Answer: $7,926.75

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)

Answer: $4,213

 

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: 

present value of annuity formula

PVA25 = 274,509.87

Bonus = 10,000

Answer: $284,509.87

 

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?

Solution: 

present value of ordinary annuity

Answer: $82,836.48

 

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?

Solution: 

present value of annuity due

Answer: $807.47

present value of an ordinary annuity

Answer: $807.48

 

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: 

present value of an annuity formula

PVA6 = $17,022.53

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

Answer: $ 12,400

 

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)

Answer: $ 29,754

 

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?

Solution: 

how to calculate present value of annuity

Answer: $792,466.36

 Option A