John finances his daughter’s college education by making deposits into a fund earning interest at an annual effective rate of 8%. For 18 years he deposits X at the beginning of each month. In the 16 th through the 19 th years, he makes a withdrawal of 25,000 at the beginning of each year. The final withdrawal reduces the fund balance to zero.

Calculate X.

• 207
• 223
• 240
• 245
• 260

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

Solution: C

[[math]] \begin{align*} (1.08)^{1/12}-1 = 0.006434 \\ \frac{1}{1.08^{15}}25,000 \ddot{a}_{\overline{4}|8\%} = X \ddot{a}_{\overline{216}|0.6434\%} \\ X= \frac{25, 000(3.57710)}{3.17217(117.2790)} = 240.38. \end{align*} [[/math]]

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