Revision as of 23:39, 18 November 2023 by Admin (Created page with "A loan of X is repaid with level annual payments at the end of each year for 10 years. You are given: *The interest paid in the first year is 3600; and *The principal repaid in the 6th year is 4871 Calculate X. <ul class="mw-excansopts"><li>44,000</li><li>45,250</li><li>46,500</li><li>48,000</li><li>50,000</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
A loan of X is repaid with level annual payments at the end of each year for 10 years.
You are given:
- The interest paid in the first year is 3600; and
- The principal repaid in the 6th year is 4871
Calculate X.
- 44,000
- 45,250
- 46,500
- 48,000
- 50,000
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
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.