Time Value of Money Problems for Money and Banking

1. Find the values for the following:
a. An initial \$500 compounded for 1 year at 6 percent.
b. An initial \$500 compounded for 2 years at 6% percent.
c. The present value of \$500 due in 1 year at a discount rate of 6 percent.
d. The present value of \$500 due in 2 years at a discount rate of 6 percent.

2. What is the monthly payment on a 6 year car loan for \$16,000 at an annual interest rate of 12%. (Hint: use the monthly interest rate).

3. In 1626, Peter Minuit purchased Manhattan Island from some Algonquian Indians for cloth, beads and trinkets worth about \$24 at the time, an apparent bargain compared with the price of Manhattan real estate today. Assume that the value of Manhattan real estate in the year 2001 is about \$60 billion, did Peter Minuit get a good deal or not? To decide, assume that Peter's \$24 could have alternatively been invested in a bank account in 1626, getting 6% interest per year, instead of being invested in Manhattan.

4. Which grows to a larger future value, \$1000 invested for 2 years at:
a. 10 percent each year
b. 5 percent the first year and 15 percent the second year or
c. 15 percent the first year and 5 percent the second year?

5. Which grows to a larger future value:
a. \$2000 invested for 20 years at 10% or
b. \$1000 invested for 20 years at 20%.

6. Which is worth more at 14 percent, compounded annually: \$1000 in hand today or \$2,000 due in 6 years?

7. A paper company invests \$4m to clear a tract of land and plant some young pine trees. The trees will mature in 10 years, at which time the forest will have a market value of \$8m. What is the expected rate of return for the paper company's investment?

8. A 1987 advertisement in the New Yorker solicited offers on a 1967 Mercury Cougar XR7 (Motor Trend's 1967 car of the year) that had been stored undriven in a climate controlled environment for 20 years. If the original owner paid \$4000 for this car in 1967, what price would he have to receive in 1987 to obtain a 10 percent annual return on his investment?

9. Vincent Van Gogh sold only one painting during his lifetime, for about \$30. A sunflower still life he painted in 1888 sold for \$39.85 million in 1988,, more than three times the highest price paid previously for any work of art. If this painting had been purchased for \$30 in 1888 and sold in 1988 for \$39.85 million, what would have been the annual rate of return?

10. In 1940, your grandmother put \$1000 into a special trust to be paid to a future grandchild (you) 60 years later, in the year 2000. How much will this trust be worth in the year 2000 if it has been earning 8%? How much if it earns 12%.

11. A "million-dollar" lottery pays \$25,000 a year for 40 years. At a 10 percent required return, what is the present value of this payoff? Assume that the first payment is paid immediately. (Calculator only)

12. You have been hired as a financial advisor to Michael Jordan. He has received two offers for playing professional basketball and wants to select the best offer, based on considerations of money only. Offer A is a "\$10m" offer for \$2m year for 5 years. Offer B is a "\$11m" offer of \$1/m year for four years and \$\$7m in year 5. Michael's required rate of return is 10%. What is your advice? (Hint: compare the present value of each contract)

13. Below are four bonds and their yields to maturity in November 1988. Which bonds were selling at a premium and which were selling at a discount (the first number is coupon rate and the second number is maturity date)?
a. Texaco 13 91, YTM = 11.9%
b. Texaco 13 5/8 94, YTM = 11.5%
c. Texaco 5 3/4 97, YTM = 10%
d. Texaco 7 3/4 01, YTM = 10.3%

14. T-F-U, explain.
a. If the coupon rate is greater than the current yld, the bond sells at a discount.
b. A bond sells at a premium when the yield is less than the coupon rate.
c. A bond sells at par when the current yield and the coupon rate are about the same.

15. What is the yield on a 10 year, \$1000 face value, zero discount bond that sells for \$485?

16. What is the price of the following bonds if current yields are 10%? (Assume a face value of \$1000)
a. An 18 year zero coupon bond.
b. A ten year 8 percent coupon bond.
c. A twenty year 12 percent coupon bond.
d. A ten year 10 percent coupon bond.

17. At an interest rate of 10%, what is present value of \$1m to be received in:
a. 10 years
b. 50 years
c. 100 years
d. 150 years

18. What is the current yield of the following bonds: (Assume face value of \$1000).
a. A bond with a ten percent coupon rate selling for \$1120.
b. a bond with a ten percent coupon rate selling for \$950.
c. a bond with a nine percent coupon rate selling at par.

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