**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: **

**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: **

PVA_{3} = 5,000 (PVIFA _{7%, 3})

PVA_{3} = 5,000 (2.6243)** **

**Answer: ****$13,121.5**

**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: **

**PVA _{6 }= $9,245.76**

PV_{2} = 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: **

PVA_{10} = 2,000 (PVIFA _{6%/2, 10*2})

PVA_{10} = 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: **

**PVA _{25 }= 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: **

**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: **

**Answer: $807.47**

**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: **

**PVA _{6 }= $17,022.53**

PV_{4} = 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: **

**Answer: $792,466.36**

** ****Option A**

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