A bond has a face value of $1,000 and coupon payments of $80 annually.This bond matures in three years and is selling for $1,000 in the market.Market interest rate is 8 percent.What is this bond's duration?
A)3 years
B)2.78 years
C)1.95 years
D)4.31 years
E)None of the options is correct.

Question

Quizplus · Accepted Answer

The bond's duration is 2.78 years. This is because the bond's present value is equal to the sum of the present values of its future cash flows, discounted at the market interest rate. The present value of the bond's coupon payments is $228.32, and the present value of the bond's face value is $771.68. The bond's duration is the weighted average of the times to maturity of its future cash flows, with the weights being the present values of the cash flows. The bond's duration is 2.78 years because the present value of the bond's coupon payments is greater than the present value of the bond's face value.

A Bond Has a Face Value of $1,000 and Coupon