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.

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.