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ABy Admin
Nov 18'23
Exercise
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.
ABy Admin
Nov 18'23
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.