Chapter 15 The Term Structure of Interest Rates
42. What is the yield to maturity of a 3-year zero coupon bond? A) 7.00% B) 9.00% C) 6.99% D) 4% E) none of the above
Answer: D Difficulty: Moderate Rationale: [(1.03)(1.04)(1.05)]1/3 - 1 = 4%.
Use the following to answer questions 43-46:
The following is a list of prices for zero coupon bonds with different maturities and par value of $1,000.
43. What is, according to the expectations theory, the expected forward rate in the third
year? A) 7.23 B) 9.37% C) 9.00% D) 10.9% E) none of the above
Answer: B Difficulty: Moderate Rationale: 862.57 / 788.66 - 1 = 9.37%
44. What is the yield to maturity on a 3-year zero coupon bond? A) 6.37% B) 9.00% C) 7.33% D) 8.24% E) none of the above
Answer: D Difficulty: Moderate Rationale: (1000 / 788.66)1/3 -1 = 8.24%
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Chapter 15 The Term Structure of Interest Rates
45. What is the price of a 4-year maturity bond with a 10% coupon rate paid annually? (Par
value = $1,000) A) $742.09 B) $1,222.09 C) $1,035.66 D) $1,141.84 E) none of the above
Answer: C Difficulty: Difficult Rationale: (1000 / 711.00)1/4 -1 = 8.9%; FV = 1000, PMT = 100, n = 4, i = 8.9, PV =
$1,035.66
46. You have purchased a 4-year maturity bond with a 9% coupon rate paid annually. The
bond has a par value of $1,000. What would the price of the bond be one year from now if the implied forward rates stay the same? A) $995.63 B) $1,108.88 C) $1,000.00 D) $1,042.78 E) none of the above
Answer: A Difficulty: Difficult Rationale: (925.16 / 711.00)]1/3 - 1.0 = 9.17%; FV = 1000, PMT = 90, n = 3, i = 9.17, PV
= $995.63
Use the following to answer question 47:
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Chapter 15 The Term Structure of Interest Rates
47. Given the bond described above, if interest were paid semi-annually (rather than
annually), and the bond continued to be priced at $917.99, the resulting effective annual yield to maturity would be: A) Less than 10% B) More than 10% C) 10% D) Cannot be determined E) None of the above
Answer: B Difficulty: Moderate Rationale: FV = 1000, PV = -917.99, PMT = 45, n = 36, i = 4.995325 (semi-annual);
(1.4995325)2 - 1 = 10.24%.
Use the following to answer questions 48-50:
48. What should the purchase price of a 2-year zero coupon bond be if it is purchased at the
beginning of year 2 and has face value of $1,000? A) $877.54 B) $888.33 C) $883.32 D) $894.21 E) $871.80
Answer: D Difficulty: Difficult Rationale: $1,000 / [(1.055)(1.06)] = $894.21
49. What would the yield to maturity be on a four-year zero coupon bond purchased today? A) 5.75% B) 6.30% C) 5.65% D) 5.25% E) none of the above.
Answer: A Difficulty: Moderate Rationale: [(1.05) (1.055) (1.06) (1.065)]1/4 - 1 = 5.75%
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Chapter 15 The Term Structure of Interest Rates
50. Calculate the price at the beginning of year 1 of an 8% annual coupon bond with face
value $1,000 and 5 years to maturity. A) $1,105.47 B) $1,131.91 C) $1,084.25 D) $1,150.01 E) $719.75
Answer: C Difficulty: Difficult Rationale: i = [(1.05) (1.055) (1.06) (1.065) (1.07)]1/5 - 1 = 6%; FV = 1000, PMT = 80, n
= 5, i = 6, PV = $1084.25
51. Given the yield on a 3 year zero-coupon bond is 7% and forward rates of 6% in year 1
and 6.5% in year 2, what must be the forward rate in year 3? A) 7.2% B) 8.6% C) 8.5% D) 6.9% E) none of the above.
Answer: C Difficulty: Moderate Rationale: f3 = (1.07)3 / [(1.06) (1.065)] - 1 = 8.5%
Use the following to answer questions 52-61:
52. What should the purchase price of a 1-year zero coupon bond be if it is purchased today
and has face value of $1,000? A) $966.37 B) $912.87 C) $950.21 D) $956.02 E) $945.51
Answer: D Difficulty: Difficult Rationale: $1,000 / (1.046) = $956.02
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Chapter 15 The Term Structure of Interest Rates
53. What should the purchase price of a 2-year zero coupon bond be if it is purchased today
and has face value of $1,000? A) $966.87 B) $911.37 C) $950.21 D) $956.02 E) $945.51
Answer: B Difficulty: Difficult Rationale: $1,000 / [(1.046)(1.049)] = $911.37
54. What should the purchase price of a 3-year zero coupon bond be if it is purchased today
and has face value of $1,000? A) $887.42 B) $871.12 C) $879.54 D) $856.02 E) $866.32
Answer: E Difficulty: Difficult Rationale: $1,000 / [(1.046)(1.049)(1.052)] = $866.32
55. What should the purchase price of a 4-year zero coupon bond be if it is purchased today
and has face value of $1,000? A) $887.42 B) $821.15 C) $879.54 D) $856.02 E) $866.32
Answer: B Difficulty: Difficult Rationale: $1,000 / [(1.046)(1.049)(1.052)(1.055)] = $821.15
56. What should the purchase price of a 5-year zero coupon bond be if it is purchased today
and has face value of $1,000? A) $776.14 B) $721.15 C) $779.54 D) $756.02 E) $766.32
Answer: A Difficulty: Difficult Rationale: $1,000 / [(1.046)(1.049)(1.052)(1.055)(1.058)] = $776.14
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