Revision as of 19:40, 18 November 2023 by Admin (Created page with "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. <ul class="mw-excansopts"><li>67,600</li><li>70,300</li><li>75,700</li><li>78,200</li><li>80,700</li>...")
ABy Admin
Nov 18'23
Exercise
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.
ABy Admin
Nov 18'23
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.