A 25-year loan is being repaid with payments of 1300 at the end of each year. The loan payments are based on an annual effective interest rate of 8%. The borrower pays an additional 4000 at the time of the fifth payment and will repay the remaining balance with a payment of X at the end of each of the subsequent ten years.

Calculate X

• 893
• 1300
• 1306
• 1500
• 1902

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: C

[[math]] \begin{array}{l}{{1300a_{\overline{{{20}}}|0.08}-4000=X a_{\overline{{{10}}}|0.08}}}\\ {{12,763.59-400=X(6.71008)=1306.03}}\end{array} [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.