Assignment

1. How much would you have to invest today to receive:

a.) $12,000 in 6 years at 12 percent?
b.) $15,000 in 15 years at 8 percent?
c.) $5,000 each year for 10 years at 8 percent?
d.) $40,000 each year for 40 years at 5 percent?

2. If you invest $8,000 per period for the following number of periods, how much would you have?

a.) 7 years at 9 percent.
b.) 40 years at 11 percent.

3. You invest a single amount of $12,000 for 5 years at 10 percent. At the end of 5 years you take the proceeds and invest them for 12 years at 15 percent. How much will you have after 17 years?

4. Mrs. Crawford will receive $6,500 a year for the next 14 years from her trust. If an 18 percent interest rate is applied, what is the current value of the future payments?

5. Sherwin Williams will receive $18,000 a year for the next 25 years as a result of a picture he has painted. If a discount rate of 10 percent is applied, should he be willing to sell out his future rights for $160,000?

6. The Western Sweepstakes has just informed you that you have won $1 million. The amount is to be paid out at the rate of $50,000 a year for the next 20 years. With a discount rate of 12 percent, what is the present value of your winnings?

7. Rita Gonzales won the $60 million lottery. She is to receive $1 million a year for the next 50 years plus an additional lump sum of $10 million after 50 years. The discount rate is 10 percent. What is the current value of her winnings?

8. Determine the amount of money in a savings account at the end of five years, given an initial deposit of $3,000 and an 8 percent annual interest rate when interest is compounded (a) annually, (b) semiannually, and (c) quarterly.

9. You wish to retire in 20 years, at which time you want to have accumulated enough money to receive an annual annuity of $12,000 for 25 years after retirement. During the period before retirement you can earn 8 percent annually, while after retirement you can earn 10 percent on your money.

What annual contributions to the retirement fund will allow you to receive the $12,000 annuity?

10. Jim Thorpe borrows $70,000 toward the purchase of a home at 12 percent interest. His mortgage is for 30 years.

a.) How much will his annual payments be? (Although home payments are usually on a monthly basis, we shall do our analysis on an annual basis for ease of computation. We will get a reasonably accurate answer.)

b.) How much interest will he pay over the life of the loan?

c.) How much should he be willing to pay to get out of a 12 percent mortgage and into a 10 percent mortgage with 30 years remaining on the mortgage? Suggestion: Find the annual savings and then discount them back to the present at the current interest rate (10 percent).