Greg buys a 20-year increasing annuity-immediate with annual payments. The first payment is 110 and each succeeding payment is equal to the previous payment plus X. The annuity is priced at 2000 based on an annual effective interest rate of 10%.

Calculate X.

• 16.64
• 17.45
• 19.19
• 21.00
• 22.68

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

Solution: C

[[math]] \begin{aligned} & 2000=110 a_{20 \mid 0.10}+X\left[\frac{a_{\overline{20} | 0.10}-20 v^{20}}{0.10}\right] \\ & 2000=110(8.51356)+X(55.40691) \\ & 1063.51=X(55.40691) \\ & X=19.1945\end{aligned}[[/math]]

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