Nov 20'23
Exercise
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.
Nov 20'23
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.