You are given the following term structure of interest rates:

Length of investment in years	Spot rate
1	7.50%
2	8.00%
3	8.50%
4	9.00%
5	9.50%

Calculate the one-year annual effective rate for the fifth year implied by this term structure.

• 9.0%
• 9.5%
• 10.0%
• 10.5%
• 11.5%

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

Solution: E

[[math]] \begin{array}{l}{{(1+s_{4})^{4}(1+{}_{1}f_{4})=(1+s_{5})^{5}}}\\ {{(1.09)^{4}(1+{}_{1}f_{4})=(1.095)^{5}}}\\ {{1f_{4}=0.1152}}\end{array} [[/math]]

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