You are given the following information:

Bond	Coupon Rate	Maturity	Price
A	10%	1	106.80
B	5%	2	101.93
C	10%	3	111.31

All coupon payments are annual and par values are 100. Compute the annual forward rate from year one to year two

• 4.5%
• 4.75%
• 5%
• 5.25%
• 5.5%

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: 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.