What is the value of a zero-coupon bond with a yield to maturity of 9 percent, a par value of $1,000, and 10 years to maturity? (Assume semi-annual compounding)
A) $208.29
B) $414.64
C) $422.41
D) $643.93
E) $910.00

Question

Quizplus · Accepted Answer

The value of a zero-coupon bond can be calculated using the formula: $ P = \frac{M}{(1 + r)^n} $, where $P$ is the price of the bond, $M$ is the maturity value (or par value), $r$ is the yield per period, and $n$ is the total number of periods. Given a yield to maturity of 9% with semi-annual compounding, the yield per period is $ \frac{9\%}{2} = 4.5\% $ or 0.045 in decimal form. With 10 years to maturity and semi-annual compounding, there are $ 10 \times 2 = 20 $ periods. Substituting these values into the formula gives $ P = \frac{1000}{(1 + 0.045)^{20}} $, which calculates to approximately $414.64.

What Is the Value of a Zero-Coupon Bond with a Yield