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ABy Admin
Nov 18'23
Exercise
A perpetuity pays X at the end of the third year, 2X at the end of the sixth year, 3X at the end of the ninth year, etc. At a 6% annual effective interest rate, the present value of the perpetuity is 655.56.
Calculate X.
- 2
- 17
- 20
- 33
- 39
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: C
First calculate the three-year interest rate.
[[math]]
1.06^3-1=0.191016
[[/math]]
This is an arithmetic increasing perpetuity.
[[math]]
\begin{aligned}
& X\left[\frac{1}{0.191016}+\frac{1}{0.191016^2}\right]=655.56 \\
& X=20.08
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.