Suppose that all investors expect that interest rates for the 4 years will be as follows: $$\begin{array} { l | l | }
\hline \text { Year } & \text { Forward Interest Rate } \
\hline 0 & \text { (today) } 5 \% \
\hline 1 & 7 \% \
\hline 2 & 9 \% \
\hline 3 & 10 \% \
\hline
\end{array}$$
-What is the price of a 2-year maturity bond with a 10% coupon rate paid annually? (Par value = $1,000)
A)$1,092
B)$1,054
C)$1,000
D)$1,073
E)none of the above

Question

Suppose that all investors expect that interest rates for the 4 years will be as follows: $$\begin{array} { l | l | } 
\hline \text { Year } & \text { Forward Interest Rate } \
\hline 0 & \text { (today) } 5 \% \
\hline 1 & 7 \% \
\hline 2 & 9 \% \
\hline 3 & 10 \% \
\hline
\end{array}$$
-What is the price of a 2-year maturity bond with a 10% coupon rate paid annually? (Par value = $1,000)
A)$1,092
B)$1,054
C)$1,000
D)$1,073
E)none of the above

Quizplus · Accepted Answer

To calculate the price of the bond, we need to discount each cash flow back to present value and then sum them up. We can use the formula:

$Price = \frac{C}{1+r_1} + \frac{C}{(1+r_2)^2} + \frac{C+Par}{(1+r_3)^3}$

where C is the coupon payment, r is the forward interest rate for the respective year, and Par is the par value of the bond. 
Substituting the given information in the formula, we get:

$Price = \frac{1000	imes0.10}{1+0.07} + \frac{1000	imes0.10}{(1+0.09)^2} + \frac{1100}{(1+0.10)^3}$
$Price = 93.46 + 76.68 + 902.16$
$Price = 1072.3$

Therefore, the price of the bond is $1,073 (rounded to the nearest dollar), so the answer is D.

Suppose That All Investors Expect That Interest Rates for the 4