An investor deposits 1000 at the beginning of each year for 20 years. The fund earns interest at an annual effective rate of 9.25%. At the end of 20 years, the investor wishes to use the fund to purchase a 30-year annuity-due with monthly payments of 500 based on an annual nominal interest rate of 10% convertible monthly.

Calculate the balance, if any, in the fund after paying for the annuity.

• The fund balance is insufficient to purchase the annuity.
• 0
• 35
• 370
• 510

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

Solution: C

[[math]] \begin{aligned} & 1000 \ddot{s}_{\overline{20} \mid 0.0925}=57,485.26 \\ & 500 \ddot{a}_{\overline{360}| \frac{10}{12} \%}=57,450.21 \\ & 57,485.26-57,450.21=35.05\end{aligned} [[/math]]

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