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# PV of Annuity Problems and Solutions

## Problem 1: Present value of annuity

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: Present value of annuity table

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)

>> Download Present Value of Annuity Table.

## Problem 3: Present value of an annuity

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: PV of annuity using intra-year discounting

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: Present value of ordinary annuity

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

Option A

## Problem 6: Present value of annuity due

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: Present value of an annuity due

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: Present value of an ordinary annuity

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: Present value of an ordinary annuity table

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: Present value of 0rdinary annuity formula application

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:

Option A

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placed the money in an account that you expect will yield a monthly compounded interest rate
of 0.75%. Money for the first of the four payments will be removed from the account exactly
15 years from now, and the last withdrawal will be made 18 years from now. You have decided
to save more by making monthly payments into the same account, yielding 0.75% interest per
month over the next 14 years beginning next month. You will take the money out of the 0.75%
per month account and place it in a 6% per annum account in 14 years and take the cash out
as needed.
Required:
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workings and commentaries explaining why you make certain assumptions and why you take
certain actions, backed with appropriate academic sources.

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