Given the bond described above,if interest were paid semi-annually (rather than annually),and the bond continued to be priced at $850,the resulting effective annual yield to maturity would be: $$\begin{array} { | l | l | }
\hline \text { Par Value } & \$ 1,000 \
\hline \text { Time to Maturity } & 20 \text { years } \
\hline \text { Coupon } & 10 \% \text { (paid annually) } \
\hline \text { Current Price } & \$ 850 \
\hline \text { Yield to Maturity } & 12 \% \
\hline
\end{array}$$
A)Less than 12%
B)More than 12%
C)12%
D)Cannot be determined
E)None of the above

Question

Given the bond described above,if interest were paid semi-annually (rather than annually),and the bond continued to be priced at $850,the resulting effective annual yield to maturity would be: $$\begin{array} { | l | l | } 
\hline \text { Par Value } & \$ 1,000 \
\hline \text { Time to Maturity } & 20 \text { years } \
\hline \text { Coupon } & 10 \% \text { (paid annually) } \
\hline \text { Current Price } & \$ 850 \
\hline \text { Yield to Maturity } & 12 \% \
\hline
\end{array}$$
A)Less than 12%
B)More than 12%
C)12%
D)Cannot be determined
E)None of the above

Quizplus · Accepted Answer

If interest is paid semi-annually, then there will be two coupon payments per year, each equal to 5% of the par value. The bond continues to be priced at $850, which is less than the par value of $1000, implying that the effective yield to maturity is greater than the coupon rate of 10%. Since interest is paid more frequently, the effective yield to maturity will be higher than the annual yield to maturity of 12%. This is because the interest earned on each coupon payment is reinvested for a longer period of time. Therefore, the resulting effective annual yield to maturity will be more than 12%, which is only possible with option B.

Given the Bond Described Above,if Interest Were Paid Semi-Annually (Rather