A level monthly contribution of X is required to purchase an annual perpetuity of 5000 that commences five years from today. The contributions are made at the end of each month for 60 months. The last contribution is made at the same time as the first payment from the perpetuity. The annual nominal interest rate is 12% compounded monthly.

Calculate X.

• 402
• 483
• 510
• 544
• 581

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

Solution: D

[[math]] \begin{aligned} & X s_{\overline{60 \mid i}}=\frac{5000}{d}=\frac{5000}{i}(1+i)=\frac{5000(1.01)^{12}}{(1.01)^{12}-1} \\ & 44,423.95=81.67 X \\ & X=543.94\end{aligned} [[/math]]

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