A payment of 55,400 made today returns payments of 10,000 at the beginning of each year for ten years. These payments are deposited into an account that earns interest at an annual effective rate of 6% payable at the end of each year. The interest is immediately reinvested at an annual effective interest rate of 4%. The original payment earns an annual effective yield rate of i over the ten-year period.

Calculate i

• 9.0%
• 9.5%
• 10.0%
• 10.5%
• 11.0%

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

Solution: B

[[math]] \begin{aligned} & 10,000(10)+\left[600 s_{\overline{10} \mid 0.04}+600 \frac{s_{\overline{10} \mid 0.04}-10}{0.04}\right]=137,295.27 \\ & 55,400(1+i)^{10}=137,295.27 \\ & i=0.095 \end{aligned} [[/math]]

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