Kevin makes a deposit at the end of each year for 10 years into a fund earning interest at a 4% annual effective rate. The first deposit is equal to X, with each subsequent deposit 9.2% greater than the previous year’s deposit. The accumulated value of the fund immediately after the 10 th deposit is 5000.

Calculate X.

• 255
• 260
• 270
• 279
• 293

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

Solution: D

Equating present values gives

[[math]] \begin{aligned} \frac{5000}{1.04^{10}}=X\left[1-\left(\frac{1.092}{1.04}\right)^{10}\right] \\ 3377.82 = X(12.094127) \\ X = 279.29 \end{aligned} [[/math]]

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