An investor wishes to accumulate 5000 in a fund at the end of 15 years. To accomplish this, she plans to make equal deposits of X at the end of each year for the first ten years. The fund earns an annual effective rate of 6% during the first ten years and 5% for the next five years.

Calculate X.

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

Solution: C

[[math]] \begin{align*} 5000 = Xs_{\overline{10}|0.06}(1.05)^5 \\ X={\frac{\,5000\,}{13.1808(1.2763)}}=297.22 \\ \end{align*} [[/math]]

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