Annual payments of 240 are made at the end of each year to repay a loan of 3400. The payments are based on an annual effective interest rate of 4.5%. The loan is settled with a drop payment of X.

Calculate X.

• 1.61
• 4.53
• 8.83
• 12.48
• 13.04

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

Solution: E

[[math]] \begin{aligned} & 3400=240 a_{\overline{n} | 0.045} \\ & n=23.05 \end{aligned} [[/math]]

Use 23 for the number of full payments of [math]240 . X[/math] will be paid at time 24 .

[[math]] \begin{aligned} & 3400=240 a_{\overline{23}| 0.045}+X v^{24} \\ & 3400=3395.47+X v^{24} \\ & 4.53=X v^{24} \\ & X=13.04 \end{aligned} [[/math]]

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