USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Consider two bonds: both pay annual interest. Bond Y has a coupon of 6 percent per year, maturity of five years, yield to maturity of 6 percent per year, and a face value of $1000. Bond X has a coupon of 7 percent per year, maturity of 10 years, yield to maturity of 4 percent per year, and a face value of $1000.
-Refer to Exhibit 13.13. Calculate the modified duration for Bond Y.
A) 7.8
B) 4.22
C) 4.34
D) 7.5
E) 9.8

Question

Quizplus · Accepted Answer

Modified duration measures the price sensitivity of a bond to a change in interest rates and is calculated as the Macaulay duration divided by (1 + yield/number of coupon periods per year). For Bond Y, with a yield to maturity of 6% and annual payments, the formula simplifies to Macaulay duration / (1 + 0.06). Given that Bond Y has a yield equal to its coupon rate, it will be priced at par, and its Macaulay duration will be close to its time to maturity adjusted for the present value of its cash flows. Without the exact Macaulay duration provided, we can infer that the correct answer must reasonably reflect a duration less than its maturity due to the discounting effect, making 4.22 the most plausible choice given the options.