$$\begin{array} { l | l }
\hline \text { Year } & \text { 1-Year Forward Rate } \
\hline 1 & 4.6 \% \
\hline 2 & 4.9 \% \
\hline 3 & 5.2 \% \
\hline 4 & 5.5 \% \
\hline 5 & 5.8 \% \
\hline
\end{array}$$
-What should the purchase price of a 5-year zero coupon bond be if it is purchased today and has face value of $1,000?
A)$776.14
B)$721.15
C)$779.54
D)$756.02
E)$766.32

Question

$$\begin{array} { l | l } 
\hline \text { Year } & \text { 1-Year Forward Rate } \
\hline 1 & 4.6 \% \
\hline 2 & 4.9 \% \
\hline 3 & 5.2 \% \
\hline 4 & 5.5 \% \
\hline 5 & 5.8 \% \
\hline
\end{array}$$
-What should the purchase price of a 5-year zero coupon bond be if it is purchased today and has face value of $1,000?
A)$776.14
B)$721.15
C)$779.54
D)$756.02
E)$766.32

Quizplus · Accepted Answer

Using the formula for calculating present value of a zero coupon bond, we have:

$$P_0 = \frac{FV}{(1 + r)^t}$$

where $P_0$ is the purchase price of the bond, $FV$ is the face value of the bond, $r$ is the annual interest rate, and $t$ is the time to maturity in years.

For the given bond, $FV = 1,000$ and $t = 5$. To find the appropriate interest rate, we need to use the 5-year forward rate, which is the interest rate for a loan that starts five years from now. Based on the given information, we know that the 5-year forward rate is 5.8%.

Plugging values into the formula, we get:

$$P_0 = \frac{1,000}{(1 + 0.058)^5} = 776.14$$

Therefore, the purchase price of the bond should be $776.14. The answer is A.

-What Should the Purchase Price of a 5-Year Zero Coupon