John deposits 1000 into a fund. The fund earns:

1. an annual nominal rate of interest of 4% convertible quarterly for the first three years;
2. a constant annual force of interest of 5% for the next three years; and
3. an annual nominal discount rate of 6% convertible semiannually thereafter.

Calculate the amount in the fund at the end of ten years.

• 1658
• 1667
• 1670
• 1674
• 1677

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

Solution: C

[[math]] \begin{aligned} & 1000\left(1+\frac{0.04}{4}\right)^{3 \times 4}\left(e^{0.05(3)}\right)\left(1-\frac{0.06}{2}\right)^{-2 \times 4} \\ & =1670.42\end{aligned} [[/math]]

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