Revision as of 20:10, 18 November 2023 by Admin (Created page with "Susan won the lottery today which will pay an annual perpetuity of X, with the first payment occurring five years from today. The perpetuity has a present value of 100,000 based on an annual effective interest rate of 1% for the first ten years and 5% for all years thereafter. Calculate X. <ul class="mw-excansopts"><li>4100</li><li>4224</li><li>4357</li><li>4401</li><li>5696</li></ul> {{soacopyright | 2023 }}")
Nov 18'23
Exercise
Susan won the lottery today which will pay an annual perpetuity of X, with the first payment occurring five years from today. The perpetuity has a present value of 100,000 based on an annual effective interest rate of 1% for the first ten years and 5% for all years thereafter.
Calculate X.
- 4100
- 4224
- 4357
- 4401
- 5696
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Nov 18'23
Solution: B
[[math]]
\begin{aligned} & 100,000=X a_{6 \mid 0.01} v_{0.01}^4+\frac{X}{0.05} v_{0.01}^{10} \\ & 100,000=X(5.79548)(0.96098)+X(20)(0.90529) \\ & 100,000=X(23.6751) \\ & X=4223.85\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.