Consider a zero-coupon bond with 20 years to maturity.The amount that the price of the bond will change if its yield to maturity decreases from 7% to 5% is closest to:

Question

Quizplus · Accepted Answer

The price of a zero-coupon bond with 20 years to maturity is calculated using the formula $P = \frac{F}{(1+y)^t}$, where $F$ is the face value of the bond, $y$ is the yield to maturity as a decimal, and $t$ is the number of years to maturity.

At a yield to maturity of 7%, the price of the bond is $P_1 = \frac{1000}{(1+0.07)^{20}} = 226.76$.

At a yield to maturity of 5%, the price of the bond is $P_2 = \frac{1000}{(1+0.05)^{20}} = 376.89$.

Therefore, the change in price is $P_2 - P_1 = 376.89 - 226.76 = 150.13$, which is closest to answer choice A ($118$).

Consider a Zero-Coupon Bond with 20 Years to Maturity