The following is a list of prices for zero coupon bonds with different maturities and par value of $1,000. $$\begin{array} { | l | l | }
\hline \text { Maturity (Years) } & \underline { \text { Price } } \
\hline 1 & \$ 943.40 \
\hline 2 & \$ 881.68 \
\hline 3 & \$ 808.88 \
\hline 4 & \$ 742.09 \
\hline
\end{array}$$
-What is the price of a 4-year maturity bond with a 12% coupon rate paid annually? (Par value = $1,000)
A)$742.09
B)$1,222.09
C)$1,000.00
D)$1,141.92
E)none of the above

Question

The following is a list of prices for zero coupon bonds with different maturities and par value of $1,000. $$\begin{array} { | l | l | } 
\hline \text { Maturity (Years) } & \underline { \text { Price } } \
\hline 1 & \$ 943.40 \
\hline 2 & \$ 881.68 \
\hline 3 & \$ 808.88 \
\hline 4 & \$ 742.09 \
\hline
\end{array}$$
-What is the price of a 4-year maturity bond with a 12% coupon rate paid annually? (Par value = $1,000)
A)$742.09
B)$1,222.09
C)$1,000.00
D)$1,141.92
E)none of the above

Quizplus · Accepted Answer

The price of a zero coupon bond is obtained from the future value of the principal and the present value of the principal.

For a 4-year maturity bond with a 12% coupon rate paid annually and a par value of $1,000: 
- The annual coupon payment is $120 ($1,000 x 12%). 
- The future value of the principal is $1,000. 
- The present value of the principal at the yield rate that corresponds to the zero coupon bond prices is $742.09 (from the table).

Therefore, the price of the bond is the sum of the present value of the principal and the present value of the coupon payments:

Price = $742.09 + ($120/1.12) + ($120/1.12^2) + ($120/1.12^3) + ($1,000/1.12^4) 
Price = $1,141.92

Thus, the best choice is D.

The Following Is a List of Prices for Zero Coupon