A perpetuity makes payments every five years with a first payment of 2 to be paid five years from now. Each subsequent payment is 10 more than the previous payment. The annual effective interest rate is 9%.

Calculate the present value of the perpetuity.

• 34.47
• 35.80
• 36.33
• 37.12
• 38.18

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: E

Let [math]j[/math] equal the five-year interest rate.

[[math]] \begin{aligned} & (1+j)=(1.09)^5 \\ & j=0.538624 \\ & P V=\frac{2}{0.538624}+\frac{10}{(0.538624)^2}=38.18 \end{aligned} [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.