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.

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.