Suppose that all investors expect that interest rates for the 4 years will be as follows: $$\begin{array} { l | l | }
\hline \text { Year } & \text { Forward Interest Rate } \
\hline 0 & \text { (today) } 3 \% \
\hline 1 & 4 \% \
\hline 2 & 5 \% \
\hline 3 & 6 \% \
\hline
\end{array}$$
-What is the price of 3-year zero coupon bond with a par value of $1,000?
A)$889.08
B)$816.58
C)$772.18
D)$765.55
E)none of the above

Question

Suppose that all investors expect that interest rates for the 4 years will be as follows: $$\begin{array} { l | l | } 
\hline \text { Year } & \text { Forward Interest Rate } \
\hline 0 & \text { (today) } 3 \% \
\hline 1 & 4 \% \
\hline 2 & 5 \% \
\hline 3 & 6 \% \
\hline
\end{array}$$
-What is the price of 3-year zero coupon bond with a par value of $1,000?
A)$889.08
B)$816.58
C)$772.18
D)$765.55
E)none of the above

Quizplus · Accepted Answer

The price of a zero-coupon bond equals the present value of the future cash flows (principal + interest payments) discounted at the appropriate interest rate. 
The appropriate interest rate here is the last available year's interest rate.

So, the price of a 3-year zero-coupon bond can be calculated as follows:

PV = $\frac{1000}{(1+6\%)^3} = 747.26$
PV = $747.26 \times (1+5\%)^2 = 816.58$
PV = $816.58 \times (1+4\%) = 849.62$
PV = $849.62 \times (1+3\%) = 889.08$

Therefore, the price of the 3-year zero-coupon bond is $889.08.

Thus, the best choice is (A).

Suppose That All Investors Expect That Interest Rates for the 4