A 10-year, zero-coupon bond with a yield to maturity of 5% has a face value of $1 000. An investor purchases the bond when it is initially traded, and then sells it five years later. What is the rate of return of this investment, assuming the yield to maturity does not change?

Question

Quizplus · Accepted Answer

The bond is purchased at a discount since it is a zero-coupon bond, so the initial price is:
$PV = \frac{	ext{Face Value}}{(1 + y)^n} = \frac{\$1 000}{(1 + 0.05)^{10}} = \$613.91$
After five years, the bond has five years left until maturity, and the price will be:
$PV = \frac{	ext{Face Value}}{(1 + y)^n} = \frac{\$1 000}{(1 + 0.05)^5} = \$781.20$
The rate of return is then:
$R = \frac{	ext{Ending Price} - 	ext{Beginning Price}}{	ext{Beginning Price}} = \frac{\$781.20 - \$613.91}{\$613.91} \approx 0.272 = 27.2\%$
However, the question is asking for the annual rate of return, so we must adjust for the five-year holding period:
$R_{	ext{annual}} = (1 + R)^{\frac{1}{n}} - 1 = (1 + 0.272)^{\frac{1}{5}} - 1 \approx 0.0401 = 4.01\%$
Therefore, the answer is (B) 4.01%.

A 10-Year, Zero-Coupon Bond with a Yield to Maturity of 5