Given the bond described above, if interest were paid semi-annually (rather than annually) and the bond continued to be priced at $917.99, the resulting effective annual yield to maturity would be $\begin{array}{lc}
\text { Par Value } & \$ 1,000 \
\text { Time to Maturity } & 18 \text { Years } \
\text { Coupon } & 9 \% \text { (paid annually) } \
\text { Current price } & \$ 917.99 \
\text { Yield to Maturity } & 12 \%
\end{array}$
A) less than 10%.
B) more than 10%.
C) 10%.
D) Cannot be determined.
E) None of the options are correct.

Question

Quizplus · Accepted Answer

If interest is paid semi-annually, then the bond will have two coupon payments per year, each equal to $45 ($1,000 par value * 9% coupon rate / 2). The semi-annual coupon rate would be 4.5% (=$45 / $1,000).

Using the semi-annual coupon rate, we can calculate the price of the bond using the same present value formula:

$917.99 = $45 / (1 + r/2) + $45 / (1 + r/2)^2 + ... + $45 / (1 + r/2)^36 + $1,000 / (1 + r/2)^36

where r is the semi-annual yield to maturity.

Solving for r using trial and error or a financial calculator, we get r = 6% (approximately).

The effective annual yield to maturity can be calculated using the formula:

(1 + r/2)^2 - 1

Plugging in r = 6%, we get an effective annual yield to maturity of 12.36%.

Since this is higher than the current yield to maturity of 12%, the answer is B (more than 10%).

Given the Bond Described Above, If Interest Were Paid Semi-Annually