$\begin{array}{cc}
\text { Year } & \text { 1-Year Forward Rate } \
1 & 4.6\% \
2 &4.9\% \
3 & 5.2\% \
4 & 5.5\% \
5 &6.8\%
\end{array}$
What is the yield to maturity of a 2-year bond?
A) 4.6%
B) 4.9%
C) 5.2%
D) 4.7%
E) 5.8%

Question

$\begin{array}{cc}
\text { Year } & \text { 1-Year Forward Rate } \
1 & 4.6\% \
2 &4.9\% \
3 & 5.2\% \
4 & 5.5\% \
5 &6.8\%
\end{array}$
 What is the yield to maturity of a 2-year bond?
A) 4.6%
B) 4.9%
C) 5.2%
D) 4.7%
E) 5.8%

Quizplus · Accepted Answer

The yield to maturity (YTM) of a 2-year bond can be calculated using the 1-year forward rates for the first and second years. The formula to calculate the YTM for a bond with a 2-year maturity, given the forward rates, is: $$ (1 + YTM)^2 = (1 + f_1)(1 + f_2) $$ where $f_1$ is the 1-year forward rate for the first year (4.6% or 0.046) and $f_2$ is the 1-year forward rate for the second year (4.9% or 0.049). Plugging in the values: $$ (1 + YTM)^2 = (1 + 0.046)(1 + 0.049) $$ $$ (1 + YTM)^2 = 1.046 \times 1.049 $$ $$ (1 + YTM)^2 \approx 1.09677 $$ $$ 1 + YTM \approx \sqrt{1.09677} $$ $$ 1 + YTM \approx 1.047 $$ $$ YTM \approx 0.047 $$ or 4.7%.

Year 1-Year Forward Rate 14.6%24.9%35.2%45.5%56.8%\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 4.6\% \\2 &4.9\% \\3 & 5.2\% \\4 & 5.5\% \\5 &6.8\%\end{array} Year 12345​ 1-Year Forward Rate 4.6%4.9%5.2%5.5%6.8%​

$\begin{array}{cc}\text { Year } & \text { 1-Year Forward Rate } \\1 & 4.6\% \\2 &4.9\% \\3 & 5.2\% \\4 & 5.5\% \\5 &6.8\%\end{array}$