Revision as of 00:10, 19 November 2023 by Admin (Created page with "A loan of 10,000 is repaid with a payment made at the end of each year for 20 years. The payments are 100, 200, 300, 400, and 500 in years 1 through 5, respectively. In the subsequent 15 years, equal annual payments of X are made. The annual effective interest rate is 5%. Calculate X. <ul class="mw-excansopts"><li>842</li><li>977</li><li>1017</li><li>1029</li><li>1075</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
A loan of 10,000 is repaid with a payment made at the end of each year for 20 years. The payments are 100, 200, 300, 400, and 500 in years 1 through 5, respectively. In the subsequent 15 years, equal annual payments of X are made.
The annual effective interest rate is 5%.
Calculate X.
- 842
- 977
- 1017
- 1029
- 1075
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: E
[[math]]
\begin{align*}
10,000=100(I a)_{\overline{{{5}}|}i}+X{\nu}^{5}a_{\overline{{{15}}}|}=100\left(\frac{\ddot{a}_{\overline{{{5}}}|}-5{\nu}^{5}}{0.05}\right)+X{\nu}^{5}a_{\overline{{{15}}|}} \\
10, 000 = 1256.64 + 8.13273X\\
1075 = X
\end{align*}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.