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ABy Admin
Nov 19'23
Exercise
A bank lends 100,000 to Sam. The loan is repaid with level payments at the end of each year for 30 years based on an annual effective interest rate of 5%. The bank reinvests the loan payments at an annual effective interest rate of 4%.
Calculate the bank’s annual effective yield rate over the 30-year period
- 4.0%
- 4.1%
- 4.2%
- 4.4%
- 4.5%
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: D
The bank’s accumulated value at the end of 30 years is:
[[math]]
\begin{aligned}
\frac{100,000}{a_{\overline{{{30}}}|0.05}}s_{\overline{{{30}}}\,0.04}=364,841 \\
100,000(1+i)^{30} = 364,481\\
i = 0.044
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.