An annuity writer sells an annual perpetuity-due, with a first payment of 3000. The payments increase by 7% annually. The purchase price, P, of the perpetuity is based on a 12% annual force of interest.

Calculate P

• 41,096
• 52,177
• 58,829
• 60,000
• 67,200

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

Solution: B

[[math]] \begin{aligned} & i=e^{0.12}-1 \\ & i=0.12749685 \\ & 3000\left[\frac{1}{0.12749685-0.07}\right](1.12749685) \\ & =58,829.14\end{aligned} [[/math]]

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