Revision as of 23:13, 18 November 2023 by Admin (Created page with "'''Solution: A''' The present value of the first eight payments is: <math display = "block"> 2000v+2000(1.03)v^{2}+...+2000(1.03)^{7}v^{8}={\frac{2000v-20000(1.03)^{8}v^{7}}{1-1.03v}} = 13,136.41. </math> The present value of the last eight payments is <math display = "block"> \begin{split} 2000(1.03)^{7}0.97v^{9}+2000(1.03)^{7}(0.97)^{2}v^{10}+\cdots+2000(1.03)^{7}(0.97^{9})v^{96} \\ =\frac{2000(1.03)^{7}0.97v^{9}-2000(1.03)^{7}(0.97)^{9}v^{17}}{1-0.97v}=7,552.2...")
Exercise
ABy Admin
Nov 18'23
Answer
Solution: A
The present value of the first eight payments is:
[[math]]
2000v+2000(1.03)v^{2}+...+2000(1.03)^{7}v^{8}={\frac{2000v-20000(1.03)^{8}v^{7}}{1-1.03v}} = 13,136.41.
[[/math]]
The present value of the last eight payments is
[[math]]
\begin{split}
2000(1.03)^{7}0.97v^{9}+2000(1.03)^{7}(0.97)^{2}v^{10}+\cdots+2000(1.03)^{7}(0.97^{9})v^{96} \\
=\frac{2000(1.03)^{7}0.97v^{9}-2000(1.03)^{7}(0.97)^{9}v^{17}}{1-0.97v}=7,552.22.
\end{split}
[[/math]]
Therefore, the total loan amount is L = 20,688.63.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.