# Money and Present Value

2. What is the present value of a security that promises to pay you $5,000 in 20 years? Assume that you can earn 7 percent if you were to invest in other securities of equal risk.

3. If you deposit money today into an account that pays 6.5 percent interest, how long will it take for you to double your money?

4. Your parents are planning to retire in 18 years. They currently have $250,000 and they would like to have $1,000,000 when they retire. What annual rate of interest would they have to earn on their $250,000 in order to reach their goal, assuming they save no more money?

5. What is the future value of a 5-year ordinary annuity that promises to pay you $300 each year? The rate of interest is 7 percent.

6. What is the future value of a 5-year annuity due that promises to pay you $300 each year? Assume that all payments are reinvested at 7 percent a year.

7. While you were a student in college, you borrowed $12,000 in student loans at an interest rate of 9 percent, compounded annually. If you repay $1,500 per year, how long, to the nearest year, will it take you to repay the loan?

8. What is the present value of a perpetuity of $100 per year if the appropriate discount rate is 7 percent? If interest rates in general were to double and the appropriate discount rate rose to 14 percent, what would happen to the present value of the perpetuity?

9. The prize in last week's Florida lottery was estimated to be worth $35 million. If you were lucky enough to win, the state will pay you $1.75 million per year over the next 20 years. Assume that the first installment is received immediately.

a. If interest rates are 8 percent, what is the present value of the prize? b. If interest rates are 8 percent, what is the future value after 20 years? c. How would your answers change if the payments were received at the end of each year?

10. Your client is 40 years old and wants to begin saving for retirement. You advise the client to put $5,000 a year into the stock market. You estimate that the market’s return will be, on average, 12 percent a year. Assume the investment will be made at the end of the year.

a. If the client follows your advice, how much money will she have by age 65? b. How much will she have by age 70?

11. The First City Bank pays 7 percent interest, compounded annually, on time deposits. The Second City Bank pays 6 percent interest, compounded quarterly.

a. Based on effective, or equivalent, interest rates, in which bank would you prefer to deposit your money? b. Could your choice of banks be influenced by the fact that you might want to withdraw your funds during the year as opposed to at the end of the year? In answering this question, assume that funds must be left on deposit during the entire compounding period in order for you to receive any interest.

12. An investment pays you 9 percent interest, compounded quarterly. What is the periodic rate of interest? What is the nominal rate of interest? What is the effective rate of interest?

13. If you deposit $750 in a money market deposit account paying 7%, how much will it be worth in 9 years?

14. You decide you would like to buy a retirement home on the Maine seacoast when you say goodbye to the working world in 40 years. The house now costs $300,000 and should go up 5% per year. What will be the cost of the house when you retire?

15. Suppose Abigail has $2,500 in her bank account today. She would like to have $30,000 saved at the end of 6 years to make a down payment on a house. If she wants to make equal annual deposits at the end of each of the next 6 years, how much should she deposit each year if the interest rate is 6%?

16. Further, suppose Abigail is able to reach her goal of owning a home. She purchased a home for $250,000, making the $30,000 down...

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