Fund J begins with a balance of 20,000 and earns an annual effective rate of 6.5%. At the end of each year, the interest earned and an additional 1000 is withdrawn from the fund so that by the end of the 20th year, the fund is depleted.

The annual withdrawals of interest and principal are deposited into Fund K, which earns an annual effective rate of 8.25%. At the end of the 20 th year, the accumulated value of Fund K is x.

Calculate x.

• 39,332
• 54,818
• 84,593
• 86,902
• 97,631

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

Solution D

Fund K receives 1000 at the end of each year and also receives interest payments of 1300, 1235, 1170, ..., 65. The accumulated value is

[[math]] \begin{align*} 1000s_{\overline{20}|0.0825} + 65D(Ds)_{\overline{20}|0.0825} \\ = 1000(47.0491) + 65 \frac{20(1.0825)^{20}-s_{\overline{20}|0.0825}}{0.0825} \\ 47, 049.1 + 65 \frac{97.6311 -47.0491}{0.0825}= 86,902. \end{align*} [[/math]]

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