An annual perpetuity pays 1 one year from now. Payments will then increase by 4% per year for 5 years and 8% per year thereafter. Calculate the present value of this perpetuity at an annual effective interest rate of 12%.

• 21.13
• 23.51
• 25.95
• 28.87
• 31.23

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

Solution: A

[[math]] \left[\frac{1-\left(\frac{1.04}{1.12}\right)^5}{0.12-0.04}\right]+\left[\left(\frac{1.04}{1.12}\right)^5\left(\frac{1}{0.12-0.08}\right)\right]=3.87+17.26=21.13 [[/math]]

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