The present value of a perpetuity-immediate with a first payment of P and successive annual increases of 9 at an annual effective interest rate of 6% is 2600.

Calculate P.

• 5.50
• 6.00
• 6.50
• 7.00
• 7.50

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

Solution: B

[[math]] \begin{aligned} 2600=P a_{\overline{\infty}|0.06}+v9(I a)_{\overline{\infty}|0.06} \\ =P{\frac{1}{0.06}}+{\frac{1}{1.06}}9{\frac{1.06}{0.06^{2}}} \\ {\frac{P}{0.06}}+2500 \\ P = (2600-2500)(0.06) =6 \end{aligned} [[/math]]

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