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.

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.