Revision as of 00:40, 19 November 2023 by Admin (Created page with "'''Solution: D''' Let P be the annual payment. The fifth line is obtained by solving a quadratic equation. <math display = "block"> \begin{array}{l c r}{P(1- v ^{10})=3600}\\ {P v ^{10-6+1}=4871}\\ {\frac{1-v^{10}}{v^5}=\frac{3600}{4871}}\\ {1- v ^{10}=0.739068 v^{5}} \\{{ v ^{5}=0.69656}}&{{}}\\ {{ v ^{10}=0.485195}}\\ i = 0.485195^{-1/10}-1=0.075 \\ X=P{\frac{1- v ^{10}}{i}}={\frac{3600}{0.075}}=48,000 \end{array} </math> {{soacopyright | 2023 }}")
Exercise
ABy Admin
Nov 19'23
Answer
Solution: D
Let P be the annual payment. The fifth line is obtained by solving a quadratic equation.
[[math]]
\begin{array}{l c r}{P(1- v ^{10})=3600}\\ {P v ^{10-6+1}=4871}\\ {\frac{1-v^{10}}{v^5}=\frac{3600}{4871}}\\ {1- v ^{10}=0.739068 v^{5}} \\{{ v ^{5}=0.69656}}&{{}}\\ {{ v ^{10}=0.485195}}\\
i = 0.485195^{-1/10}-1=0.075
\\ X=P{\frac{1- v ^{10}}{i}}={\frac{3600}{0.075}}=48,000
\end{array}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.