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?
Explain your results.
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.