Nov 18'23
Exercise
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.
Nov 18'23
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.