A worker is starting an endowment fund for his charity. The fund will accumulate at a nominal annual interest rate of 12% convertible monthly. Beginning today, the worker will deposit 500 monthly for ten years. No deposits or withdrawals will be made for the subsequent ten years. Exactly twenty years from today, monthly payments of X will be made to his charity and continue forever.

Calculate X.

• 3270
• 3572
• 3758
• 3796
• 3834

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

Solution: D

Value of fund after 20 years:

[[math]] \begin{aligned} 500\ddot{s}_{\overline{{{120}}|0.01}}(1.01)^{120}=383,404.42 \\ 383,404.42=\frac{X}{d}=\frac{X}{i}(1+i)=\frac{X}{0.01}(1.01) \\ X = 3796.08. \end{aligned} [[/math]]

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