The Wall Street Journal gives the following prices for zero coupon bonds (with a principal of 100):

Bond	Maturity Year	Price
A	1	95.92
B	2	92.01
C	3	87.00

Compute the yield to maturity of a 2-year coupon bond with a principal of 100 and a coupon rate of 4.25%. Assume annual coupon payments.

• 4%
• 4.25%
• 4.5%
• 4.75%
• 5%

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

Solution: B

[[math]] \begin{gathered}95.92=\frac{100}{1+r_1} \\ 92.01=\frac{100}{\left(1+r_2\right)^2} \\ 87.00=\frac{100}{\left(1+r_3\right)^3} \\ r_1=\frac{100}{95.92}-1=4.25 \% \\ r_2=\left(\frac{100}{92.01}\right)^{1 / 2}-1=4.25 \% \\ r_3=\left(\frac{100}{87.00}\right)^{1 / 3}-1=4.75 \%\end{gathered} [[/math]]

The yield to maturity is simply 4.25% since the one year and two year spot rates are roughly equivalent, more specifically when we calculate the present value of a coupon bond with a coupon rate of 4.25% this bond has a current price at par.

[[math]] \begin{aligned} P V & =\frac{4.25}{1+r_1}+\frac{104.25}{\left(1+r_2\right)^2} \\ & =\frac{4.25}{1.0425}+\frac{104.25}{(1.0425)^2}=100\end{aligned} [[/math]]

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.