A 20-year zero coupon bond with a face value of $1,000 is currently selling for $214.55.Using the bond's modified duration, what is the approximate change in the price of the bond if interest rates rise by 25 basis points?

Question

Quizplus · Accepted Answer

The modified duration of a 20-year zero coupon bond is equal to its time to maturity, which is 20 years. Therefore, the approximate change in the price of the bond if interest rates rise by 25 basis points (0.25%) can be calculated as follows:
Approximate change in price = -modified duration x change in yield
= -20 x 0.0025
= -0.05 (or -5%)
Thus, the price of the bond would fall by approximately 5% if interest rates rise by 25 basis points. Choice D is the closest option at -4.63%.

A 20-Year Zero Coupon Bond with a Face Value of $1,000