**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**

This is very interesting, You’re a very skilled blogger. I’ve joined your rss feed and look forward to seeking more of your excellent post. Also, I have shared your site in my social networks!

I simply had to say thanks yet again. I do not know the things I would have made to happen in the absence of those ways contributed by you relating to such a theme. It previously was a real terrifying circumstance in my circumstances, but noticing your specialized fashion you processed the issue forced me to jump with gladness. I’m happy for your information and then believe you comprehend what a powerful job that you’re getting into educating some other people through the use of a web site. I know that you have never come across any of us.