A 20-year zero coupon bond with a face value of $1,000 is currently selling for $214.55 and has a market rate of interest of 8%. Using the bond's modified duration, what is the approximate change in the price of the bond if interest rates rise to 9%?

Question

Quizplus · Accepted Answer

First, calculate the bond's modified duration:

$$	ext{Modified Duration} = \frac{	ext{Macaulay Duration}}{(1 + r)}$$

where $r$ is the market rate of interest and the Macaulay Duration is:

$$	ext{Macaulay Duration} = \frac{20}{(1 + r)^{20}}$$

Plugging in $r = 8\%$:

$$	ext{Macaulay Duration} = \frac{20}{(1 + 0.08)^{20}} \approx 11.10$$

Then, solve for the approximate change in price:

$$	ext{Approximate Price Change} = -	ext{Modified Duration} 	imes 	ext{Change in Yield} 	imes 	ext{Original Price}$$

where the change in yield is:

$$	ext{Change in Yield} = 0.09 - 0.08 = 0.01$$

Plugging in the values:

$$	ext{Approximate Price Change} = -11.10 	imes 0.01 	imes 214.55 \approx -\$39.73$$

Therefore, the price of the bond is expected to decrease by approximately $39.73 if the interest rate rises to 9%. The answer is (C).

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