1000 is deposited into Fund X, which earns an annual effective rate of 6%. At the end of each year, the interest earned plus an additional 100 is withdrawn from the fund. At the end of the tenth year, the fund is depleted. The annual withdrawals of interest and principal are deposited into Fund Y, which earns an annual effective rate of 9%.

Calculate the accumulated value of Fund Y at the end of year 10.

• 1519
• 1819
• 2085
• 2273
• 2431

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

Solution: C

The interest earned is a decreasing annuity of 6, 5.4, etc. Combined with the annual deposits of 100, the accumulated value in fund Y is

[[math]] \begin{align*} &= 6(D s)_{\overline{{{10}}}|0.09}+100s_{\overline{{{10}}}|0.09}\\ &=6\left(\frac{10\left(1.09\right)^{10}-s_{\overline{{{10}}}|0.09}}{0.09}\right)+100\bigl(15.19293\bigr) \\ &= 565.38 + 1519.29 \\ &= 2084.67. \end{align*} [[/math]]

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