Given a 3-year,8.0% annual coupon bond with a par value of $1,000,what is the bond's Macaulay duration if the yield to maturity is 9.5%?
A) 2.779
B) 2.634
C) 2.535
D) 2.442

Question

Quizplus · Accepted Answer

The Macaulay duration of a bond is a measure of its price sensitivity to changes in interest rates. It is calculated as the weighted average of the times to maturity of the bond's cash flows, with the weights being the present values of the cash flows.In this case, the bond has a par value of $1,000, an 8.0% annual coupon rate, and a 3-year maturity. The yield to maturity is 9.5%.The present value of the bond's cash flows can be calculated as follows:PV = $1,000 / (1 + 0.095)^3 + $80 / (1 + 0.095) + $80 / (1 + 0.095)^2 + $80 / (1 + 0.095)^3= $1,000 / 1.2882 + $80 / 1.095 + $80 / 1.1941 + $80 / 1.2983= $776.92 + $73.03 + $67.01 + $61.67= $978.63The Macaulay duration of the bond can be calculated as follows:MD = (PV1 * T1 + PV2 * T2 + PV3 * T3 + PV4 * T4) / PV= ($776.92 * 3 + $73.03 * 2 + $67.01 * 1 + $61.67 * 0) / $978.63= $2.779Therefore, the bond's Macaulay duration is 2.779 years.

Given a 3-Year,8