The one-year forward rates, deferred t years, are estimated to be:

Year (t)	0	1	2	3	4
Forward Rate	4%	6%	8%	10%	12%

Calculate the spot rate for a zero-coupon bond maturing three years from now.

• 4%
• 5%
• 6%
• 7%
• 8%

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: C

[[math]] \begin{array}{c}{{s_1=_{1}f_{0} = 0.04 }}\\ {{_{1}f_{1}=0.06=\frac{\left(1+s_{2}\right)^{2}}{\left(1+s_{1}\right)^{2}}-1\Rightarrow s_{2}=\sqrt{(1.06)(1.04995)^{2}})^{1/3}-1=0.04995}}\\ {{\mathrm{}_{1}f_{2}=0.08=\frac{\left(1+s_{2}\right)^{2}}{\left(1+s_{2}\right)^{2}}-1\Rightarrow s_{3}=\mathrm{}\left((1.08\right)(1.04995)^{2}-1=0.05987=6\%.}}\end{array} [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.