Solution: C

[[math]]\begin{gathered}r_1=\frac{110}{106.8}-1=3.00 \% \\ 101.93=\frac{5}{1+r_1}+\frac{105}{\left(1+r_2\right)^2} \Rightarrow r_2=4.00 \% \\ 111.31=\frac{10}{1+r_1}+\frac{10}{\left(1+r_2\right)^2}+\frac{110}{\left(1+r_3\right)^3} \Rightarrow r_3=6.00 \%\end{gathered}[[/math]]

And the forward rate from year 1 to year 2 equals:

[[math]]f_2=\frac{\left(1+r_2\right)^2}{1+r_1}-1=5.0 \%[[/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.

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.