Chapter 6 Financial Institutions

11. To the nearest dollar, what is the value today of an investment that pays $1,000,000 in 15 years, assuming an annual opportunity cost of 8%? a. $555,265 b. $315,242 c. $463,193 d. $3,238,387 e. None of the above

b. $315,242

34. A bank buys a $10,000 Treasury bill with a maturity of 1 year. Current market rates are 8%. If interest rates rise to 8.25%, what is the approximate change in the price of the T-bill? a. -0.02% b. -0.23% c. -2.31% d. -23.15% e. -231.15%

b. -0.23% ΔP/P = -[Duration/(1+i)]*Δi = [1/(1+.08)]*.0025 = -.00231

2. If you invest $2,000 today at 9% compounded interest for two years, the value of the investment to the nearest dollar at the end of the two years will be: a. $2,376 b. $2,360 c. $2,180. d. $1,640. e. $1,624.

a. $2,376

10. To the nearest dollar, what is the value today of an investment that pays $10,000 in five years, assuming an annual opportunity cost of 6%? a. $7,473 b. $11,592 c. $8,626 d. $7,130 e. None of the above

a. $7,473

16. A bank quotes you an effective annual rate of 10% on a semi-annual investment. What is the annual simple interest rate? a. 9.76% b. 10.00% c. 10.25% d. 10.79% e. 10.96%

a. 9.76% Effective Rate = .10 = (1 + NOM/2)2 - 1 and solve for NOM. .10 + 1 = (1 + NOM/2)2 1.1 = (1 + NOM/2)2 1.11/2 = 1 + NOM/2 1.0488 = 1 + NOM/2 1.0488 - 1 = NOM/2 .0488 = NOM/2 2 * .0488 = NOM .0976 = NOM

27. Which of the following is false? a. As interest rates rise, bond prices rise, everything else the same. b. Given an absolute change in interest rates, the percentage increase in a bond's price will be greater than the percentage decrease, everything else the same. c. Long-term bonds change proportionately more in price than short-term bonds for a given rate change, everything else the same. d. A bond with a lower coupon will change more in price than a bond with a higher coupon, everything else the same. e. A bond's duration is a measure of its price elasticity.

a. As interest rates rise, bond prices rise, everything else the same.

20. Two bonds with different coupon amounts are priced to yield the same yield to maturity. For a given change in market rate: a. the bond with the lower coupon will always change more in price than the bond with the higher coupon. b. the bond with the higher coupon will always change more in price than the bond with the lower coupon. c. the bond with the lower coupon rate will only change more in price than the bond with the higher coupon rate if the market rate decreases. d. The bond with the higher coupon rate will only change more in price than the bond with the lower coupon rate if the market rate increases. e. the price change will be the same for both bonds.

a. the bond with the lower coupon will always change more in price than the bond with the higher coupon.

7. If a bond is a premium bond, then: a. the yield to maturity is less than the coupon rate. b. the yield to maturity is greater than the coupon rate. c. the yield to maturity is equal to the coupon rate. d. its duration must be greater than its maturity. e. its duration must be equal to its maturity.

a. the yield to maturity is less than the coupon rate.

32. A 90-day Treasury bill is quoted as having a 6% bond equivalent yield. What is the effective annual yield? a. 6.00% b. 6.14% c. 6.23% d. 6.62% e. 6.79%

b. 6.14%

19. For the same change in interest rates bondholder's will realize: a. a greater capital gain when rates rise than capital loss when rates fall b. a greater capital gain when rates fall than capital loss when rates rise c. a greater capital loss when rates rise than capital gain when rates fall d. a greater capital loss when rates fall than capital gain when rates rise e. the same capital gain or loss when rates rise or fall

b. a greater capital gain when rates fall than capital loss when rates rise

1. Cash in your possession today: a. is worth less than the same amount of cash received in the future. b. is worth more than the same amount of cash received in the future. c. Is worth the same as the same amount of cash to be received in the future. d. may be worth more or less than the same amount of cash received in the future depending on the market interest rate. e. may be worth more or less than the same amount of cash received in the future depending on the type of investment made.

b. is worth more than the same amount of cash received in the future.

6. If a bond is a discount bond, then: a. the yield to maturity is less than the coupon rate. b. the yield to maturity is greater than the coupon rate. c. the yield to maturity is equal to the coupon rate. d. its duration must be greater than its maturity. e. its duration must be equal to its maturity.

b. the yield to maturity is greater than the coupon rate.

12. How much would you pay for a security that pays $150 at the end of each of the next three years plus another $500 at the end of the third year if the relevant interest rate is 9%? a. $618 b. $628 c. $765 d. $950 e. None of the above

c. $765

9. To the nearest dollar, what is the value today of an investment that pays $15,000 in seven years, assuming an annual opportunity cost of 9%? a. $7,473 b. $27,421 c. $8,206 d. $7,130 e. None of the above

c. $8,206

29. A bond's Macaulay duration is 7.95 years. If the current annual interest rate is 7%, what is the modified duration of this bond? a. 7.00 years b. 7.88 years c. 7.43 years d. 7.95 years e. 8.51 years

c. 7.43 years Modified Duration = Macaulay's Duration/(1+i) = 7.95/1.07 = 7.43

13. What is the effective annual rate of an investment that offers 8%, compounded quarterly? a. 8.00% b. 8.16% c. 8.24% d. 8.32% e. 8.64%

c. 8.24%

4. If $1,500 is invested today, the initial investment plus interest will be worth $2,700 in seven years. What is the annual interest rate on the investment? a. 6.51% b. 8.05%. c. 8.76%. d. 9.12%. e. 10.43%

c. 8.76%.

5. If $2,500 is invested today, the initial investment plus interest will be worth $5,000 in eight years. What is the annual interest rate on the investment? a. 1.09% b. 5.00%. c. 9.05%. d. 10.00%. e. 20.90%

c. 9.05%.

28. Everything else the same, if the yield to maturity decreased 1 percentage point, which of the following bonds would have the largest percentage increase in value? a. A 25-year 11% coupon bond. b. A 25-year 7.5% coupon bond. c. A 25-year zero-coupon bond. d. A 3-year zero coupon bond. e. A 3-year bond with a 7.5% coupon.

c. A 25-year zero-coupon bond.

8. If a bond is a par bond, then: a. the yield to maturity is less than the coupon rate. b. the yield to maturity is greater than the coupon rate. c. the yield to maturity is equal to the coupon rate. d. its duration must be greater than its maturity. e. its duration must be equal to its maturity.

c. the yield to maturity is equal to the coupon rate.

3. If you invest $3,000 today at 8% compounded interest for three years, the value of the investment to the nearest dollar at the end of the three years will be: a. $3,000 b. $3,240 c. $3,720. d. $3,779. e. $4,081.

d. $3,779.

14. What is the effective annual cost of a credit card that charges 18%, compounded monthly? a. 16.63% b. 18.00% c. 18.81% d. 19.56% e. 19.61%

d. 19.56%

30. A three-year 9% bond is trading at par of $5,000. If you buy the bond expecting to hold it to maturity and believe you can reinvest the $225 semi-annual coupon payments at a 3.5% semi-annual rate through maturity. The total return on this investment is _____ annually. a. 3.50% b. 4.50% c. 7.00% d. 8.80% e. 9.00%

d. 8.80% Future value = $225[(1.035) 6 - 1]/0.035 = $1,473.78 + $5,000.00 = $6,473.78 Total return = [$6,473.78/$5,000.00] 1/6 - 1= 1.043994 - 1 = .043994 x 2 = 8.80%

35. Which of the following are sources of a bond's total return? a. Coupon interest b. Reinvestment income c. Capital gains or losses realize at maturity d. All of the above are sources of a bond's total return e. a. and c. only

d. All of the above are sources of a bond's total return

33. A stripped security: a. pays no interest. b. has no par value. c. is easier to value than a traditional bond. d. should sell as a package of zero coupon bonds. e. None of the above

d. should sell as a package of zero coupon bonds.

15. A bank quotes you a rate of 7% on a CD, compounded quarterly. What is the effective annual rate? a. 6.79% b. 6.81% c. 6.87% d. 7.13% e. 7.19%

e. 7.19% Effective Rate = (1 + .07/4)4 - 1 = .0719

22. The Macaulay's duration of a 10-year, 10% bond with a face value of $1,000 and a market rate of 8%, compounded annually is: a. 10 years b. 11 years c. 12 years d. 13 years e. None of the above

e. None of the above

21. Duration: a. is always greater than maturity. b. rises as the coupon payment rises. c. measures how bond prices change with changes in maturity. d. is a measure of total return. e. is a measure of how price sensitive a bond is to a change in interest rates.

e. is a measure of how price sensitive a bond is to a change in interest rates.

31. A 90-day Treasury bill is quoted as having a price of $987.50. What is its bond equivalent yield? f. 5.00% g. 5.13% h. 5.23% i. 5.62% j. 5.79%

g. 5.13%