$$\begin{array} { | l | l | }
\hline \text { Par Value } & \$ 1,000 \
\hline \text { Time to Maturity } & 18 \text { years } \
\hline \text { Coupon } & 9 ^ { \circ } \% ( \text { paid annually) } \
\hline \text { Current Price } & \$ 917.99 \
\hline \text { Yield to Maturity } & 10 ^ { \circ } \% \
\hline
\end{array}$$
-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:
A)Less than 10%
B)More than 10%
C)10%
D)Cannot be determined
E)None of the above

Question

$$\begin{array} { | l | l | } 
\hline \text { Par Value } & \$ 1,000 \
\hline \text { Time to Maturity } & 18 \text { years } \
\hline \text { Coupon } & 9 ^ { \circ } \% ( \text { paid annually) } \
\hline \text { Current Price } & \$ 917.99 \
\hline \text { Yield to Maturity } & 10 ^ { \circ } \% \
\hline
\end{array}$$
-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:
A)Less than 10%
B)More than 10%
C)10%
D)Cannot be determined
E)None of the above

Quizplus · Accepted Answer

When interest is paid semi-annually, we need to adjust the coupon rate and the number of periods to maturity accordingly. The coupon rate becomes 4.5% (9%/2) per half-year, and there are now 36 (18*2) half-year periods to maturity.

Using the bond pricing formula with semi-annual periods:

$917.99 = \frac{45}{1+(r/2)^1} + \frac{45}{1+(r/2)^2} + ... + \frac{45+1000}{1+(r/2)^{36}}$

where r is the semi-annual yield to maturity.

We can solve for r using a financial calculator or Excel:

r = 5.25% (semi-annual)

To convert this semi-annual yield to an effective annual yield, we can use the following formula:

Effective annual yield = (1 + semi-annual yield)^2 - 1

Plugging in the semi-annual yield we just calculated:

Effective annual yield = (1 + 0.0525)^2 - 1 = 10.81%

Therefore, the resulting effective annual yield to maturity would be more than 10%.

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