A perpetuity-due with annual payments is priced at X based on an annual effective interest rate of 7%. The amount of the first payment is 350. Each payment, from the second through the thirtieth, is 3% larger than the previous payment. Starting with the 31st payment, each payment is equal to the 30th payment.

Calculate X.

• 7508
• 7855
• 7925
• 7971
• 8033

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

Solution: E

Break this into two parts – the first 30 increasing payments and the remaining level perpetuity.

[[math]]350\left[\frac{1-\left(\frac{1.03}{1.07}\right)^{30}}{0.07-0.03}\right](1.07)+v^{29}\left(\frac{1}{0.07}\right) 350(1.03)^{29}=8033.38[[/math]]

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