Jill buys a 5-year bond with a 10% annual coupon rate and $1,000 maturity value, and the YTM is 10%. What is the bond's duration and modified duration?

Question

Quizplus · Accepted Answer

Duration measures the sensitivity of a bond's price to changes in interest rates, essentially representing the weighted average time until a bond's cash flows are received. Modified duration adjusts this figure to account for changes in yield. For a bond with a 10% annual coupon rate, $1,000 face value, a 5-year maturity, and a yield to maturity (YTM) of 10%, both the duration and modified duration can be calculated using financial formulas. Given that the bond's coupon rate equals its YTM, the bond would be priced at par value, simplifying the calculation. The duration of such a bond is typically less than its maturity because the investor receives some of the investment back before maturity through the coupon payments. The modified duration is lower than the duration because it accounts for the change in yield. The correct answer, 4.17 for duration and 3.79 for modified duration, reflects these principles.

Jill Buys a 5-Year Bond with a 10% Annual Coupon