Problem Set 1

Present Value Basics

1. Deposit $5000 today in an account paying 12% per year. How much will you have in six years?

2. Suppose you need $20,000 in three years to pay tuition at MU. If you can earn 8% on your money, how much do you need to set aside in savings today?

3. Deposit $5000 today in an account paying r. If we will get $10,000 in 10 years, what rate of return are we being offered?

4. Deposit $3000 today in an account paying 10%. If you will need $8000, how long will you have to wait?

5. Rarely Prudent, Inc. has an unfunded pension liability of $225 million that must be paid in 17 years. If the relevant discount rate is 8.5%, what is the present value of this liability?

6. Youre trying to choose between two different investments, both of which have up-front costs of $25,000. Investment A returns $40,000 in six years. Investment B returns $60,000 in 11 years. Which of these investments has the higher rate of return?

Multiple Cash Flows

7. You will be receiving the following payments from a friend -- $100 one year from now, $145 two years from now, and $125 three years from now. Calculate the present value of these payments given that the rate of interest is 6% per year. Also, calculate the future value of the payments in year three.

8a. Someone wants you to lend her $3000 today. She promises to pay you $1000 one year from today, $1050 two years from today and $1100 three years from today. Alternatively, you can earn 3% compounded annually by putting the money in a savings account. Should you lend her the money?

8b. How large should the last payment be, the first two being the same as in part 2a, for you to be willing to lend her the money?

9. You have the chance to buy a used widget-making machine for $200. You estimate that it will last for two more years, after which it will be worthless, but that it will bring in $150 revenue during each of those two years. If the interest rate is 8% per year, should you buy it?

10. You are the number one free agent in the National Hackey-Sack League. You get offered three different 5-year contracts, denoted A, B, and C below. Assuming you can earn 12% per year on your investments, which contract should you take?

Contract A: You are offered $100,000 today, $200,000 in one year, and a final payment of $200,000 in five years.

Contract B: You will get $200,000 today, $200,000 in three years, and a final payment of $100,000 in five years.

Contract C: You will get $100,000 each of the next five years.

Annuities, Perpetuities, and Effective Annual Rate

11. Jim invests $100 at the end of every year for the next 25 years. What is the future value of his investment at the end of 25 years? What is the present value of the investment? The APR is 8%.

12. A former alumni proposes to endow a chair at ISU. The endowment would give the university $200,000 annually as interest. The annual interest rate is 6%. What is the size of the endowment? Now the Dean points out that inflation averages about 3% per year. If the donor would like the $200,000 interest payment to grow at a rate of 3% per year in order to provide for an annual cost of living increase, then how large must the initial endowment be?

13. Calculate the future value of $100 invested at a 10% annual rate for five years when interest is compounded annually. Now re-compute the future value when interest is instead compounded either semi-annually, quarterly, monthly, or continuously.

14. You have applied for a 20-year mortgage in the amount of $120,000 to finance the purchase of a new home. If the bank will require you to make payments on a monthly basis, and the interest rate is 10%, how much can you expect to pay each month?

15. Your company will generate $27,000 annual payments each year for the next eight years from a new information database. The computer system needed to set up the database costs $180,000. If you can borrow the money to buy the computer system at 7% annual interest, can you afford the new system?

16. You will be receiving the following payments: $100 in one year, $145 in two years, and $125 in three years. Calculate the present value given an interest rate of 6% per year compounded monthly.

17. You want to buy a used Lexus for $26,500. The bank has quoted you an 11.9% APR for a 60-month loan to buy the car. What will your monthly payment be? What is the effective annual rate on this loan?

18. Find the present value of a 4-year ordinary annuity that makes payments of $500 per year. The annual discount rate is 7%. Also, find the present value if it is an annuity due.

19. Toyota has announced that it will offer free financing for 36-month loans on selected new models. How much is the zero-interest offer worth to you on a 36-month $25,000 loan if the market rate on loans of this type is 8%? If you had the option of receiving a $2,500 instant rebate instead of the zero-interest loan, would you take the rebate?

20. You have an aunt who is 55 years old. She is going to retire when she turns 65; that is, ten years from now. She would like to have an annual income of $30,000 from age 66 to 75. She would also like to have a bank balance of $100,000 at age 75. She wants you to find out how much she needs to save every year from age 56 to age 65 to make this possible. Assume an interest rate of 6% compounded annually.

Please show work!!!