Revision as of 19:45, 18 November 2023 by Admin (Created page with "'''Solution: D''' <math display = "block"> \begin{aligned} & F V=100\left[\frac{1-\left(\frac{0.9}{1.03}\right)^{20}}{0.03+0.10}\right](1.03)^{20} \\ & F V=1295.80 \end{aligned} </math> Alternatively, <math display = "block"> F V=100\left[(1.03)^{19}+0.9(1.03)^{18}+\cdots+(0.9)^{19}(1.03)^0\right]=100 \frac{(1.03)^{19}-(0.9)^{20}(1.03)^{-1}}{1-0.9(1.03)^{-1}}=1295.80 </math> {{soacopyright | 2023 }}")
Exercise
ABy Admin
Nov 18'23
Answer
Solution: D
[[math]]
\begin{aligned}
& F V=100\left[\frac{1-\left(\frac{0.9}{1.03}\right)^{20}}{0.03+0.10}\right](1.03)^{20} \\
& F V=1295.80
\end{aligned}
[[/math]]
Alternatively,
[[math]]
F V=100\left[(1.03)^{19}+0.9(1.03)^{18}+\cdots+(0.9)^{19}(1.03)^0\right]=100 \frac{(1.03)^{19}-(0.9)^{20}(1.03)^{-1}}{1-0.9(1.03)^{-1}}=1295.80
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.