USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
A $1000 par value bond with five years to maturity and a 6 percent coupon has a yield to maturity of 8 percent. Interest is paid semiannually.
-Refer to Exhibit 13.1. Calculate the modified duration for the bond.
A) 4.19 years
B) 4.36 years
C) 8.72 years
D) 8.38 years
E) 9.52 years

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 + y/n), where y is the yield to maturity and n is the number of compounding periods per year. For this bond, first, calculate the Macaulay duration, which involves finding the present value of each cash flow (interest and principal payments) and then weighting these by the time until each cash flow occurs. Given the semiannual interest payments, n = 2, and the yield to maturity needs to be adjusted accordingly to a semiannual rate, which is 4% (8% annual yield divided by 2). After calculating the Macaulay duration, divide it by (1 + 0.04) to get the modified duration. The correct answer, 4.19 years, suggests that for a 1% change in yield, the bond's price will change by approximately 4.19%. This calculation requires detailed steps involving the present value of cash flows and weighting, which are not fully shown here but lead to the correct answer of 4.19 years.