On his 65th birthday, an investor withdrew an amount P from a fund of 1,000,000 and withdrew the same amount on each successive birthday. On the date of his 82nd birthday, the fund was again equal to 1,000,000 after the withdrawal.

The fund earns an annual effective interest rate of 10%.

Calculate P.

• 81,655
• 88,915
• 90,909
• 98,879
• 109,729

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

Solution: B

[[math]] \begin{aligned} & 1,000,000(1.10)^{17}-P s_{\overline{180}| 0.10}=1,000,000 \\ & 5,054,470.285-P(45.59917)=1,000,000 \\ & 4,054,470.285=P(45.59917) \\ & P=88,915.43\end{aligned} [[/math]]

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