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 X.
A) 4.22
B) 7.8
C) 7.5
D) 9.2
E) 4.34

Question

Quizplus · Accepted Answer

The formula for modified duration is: 
Modified duration = (Macaulay duration) / (1 + yield to maturity)
Using the formula:
Macaulay duration for Bond X is: 
((1 x 1000) / (1.04^1)) + ((2 x 1000) / (1.04^2)) + ((3 x 1000) / (1.04^3)) + ((4 x 1000) / (1.04^4)) + ((5 x 1000) / (1.04^5)) + ((6 x 1000) / (1.04^6)) + ((7 x 1000) / (1.04^7)) + ((8 x 1000) / (1.04^8)) + ((9 x 1000) / (1.04^9)) + ((10 x 1000 + 1000) / (1.04^10)) 
= 8.57 years.

Modified duration for Bond X is: 
8.57 / (1 + 0.04) = 7.5 years.