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.

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.