At the beginning of each year, a payment of 5000 is invested in a fund. The payments earn an annual effective interest rate of 8%. At the end of each year, the interest is reinvested in the fund at an annual effective interest rate of 5%. The amount in the fund at the end of ten years, immediately prior to the 11 th annual payment, is X.

Calculate X to the nearest 100.

• 67,600
• 70,300
• 75,700
• 78,200
• 80,700

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

Solution: C

[[math]] \begin{aligned} & X=5000\left[10+0.08(I s)_{\overline{10} \mid 0.05}\right] \\ & X=5000\left[10+0.08\left(\frac{\ddot{s}_{\overline{10} \mid 0.05}-10}{0.05}\right)\right] \\ & X=75,654.30\end{aligned} [[/math]]

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