$\begin{array}{cc}
\text { Year } & \text { 1-Year Forward Rate } \
1 & 5\% \
2 & 5.5\% \
3 & 6.0\% \
4 & 6.5\% \
5 & 7.0\%
\end{array}$
What would the yield to maturity be on a four-year zero-coupon bond purchased today?
A) 5.75%
B) 6.30%
C) 5.65%
D) 5.25%

Question

$\begin{array}{cc}
\text { Year } & \text { 1-Year Forward Rate } \
1 & 5\% \
2 & 5.5\% \
3 & 6.0\% \
4 & 6.5\% \
5 & 7.0\%
\end{array}$
 What would the yield to maturity be on a four-year zero-coupon bond purchased today?
A) 5.75%
B) 6.30%
C) 5.65%
D) 5.25%

Quizplus · Accepted Answer

The yield to maturity (YTM) for a zero-coupon bond is the geometric average of the forward rates. For a four-year bond, the YTM is $(1.05 \times 1.055 \times 1.06 \times 1.065)^{1/4} - 1$, which approximates to 5.75%.

Year 1-Year Forward Rate 15%25.5%36.0%46.5%57.0%\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 5\% \\2 & 5.5\% \\3 & 6.0\% \\4 & 6.5\% \\5 & 7.0\%\end{array} Year 12345​ 1-Year Forward Rate 5%5.5%6.0%6.5%7.0%​

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 5\% \\2 & 5.5\% \\3 & 6.0\% \\4 & 6.5\% \\5 & 7.0\%\end{array}$