Question

Two years ago, you purchased a bond for $1036.67. The bond had two years to maturity, a coupon rate of 8%, paid annually, and a face value of $1,000. Each year, you reinvested all coupon interest at the prevailing reinvestment rate shown in the table below. Today is the bond's maturity date. What is your realized compound yield on the bond?

Time |
Prevailing Reinvestment Rate |

0 (purchase date) |
6.0% |

End of Year 1 |
7.2% |

End of Year 2 (maturity date) |
8.2% |

Select one:

a. 6.04%

b. 6.43%

c. 6.00%

d. 7.03%

e. 5.96%

Answer #1

Purchase price (P) = 1,036.67

Annual coupon (C) = coupon rate*face value = 8%*1,000 = 80

1st coupon received at the end of Year 1 is reinvested for a year at 7.2%, so reinvested coupon at the end of Year 2 is 80*(1+7.2%) = 85.76

Amount received at maturity = coupon + par value = 80 + 1,000 = 1,080

Total amount at maturity (TA) = 1,080 + 85.76 = 1,165.76

Realized compound yield = [(TA/P)^(1/n)] -1 where n = number of years of investment = 2

= [(1,165.76/1,036.67)^(1/2)]-1 = 6.04% (Option a)

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