A loan is originally scheduled to be paid in installments of 1000 payable at the end of each month for three years. The amortization is calculated with an annual nominal interest rate of 9% convertible monthly. After paying one full year of scheduled installments, the borrower increases monthly payments to 2000, resulting in a final drop payment.

Calculate the number of months after the first year that it takes for the borrower to pay off the loan.

• 10
• 11
• 12
• 13
• 14

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

Solution: C

[[math]] \begin{aligned} & O B_{12}=1000 a_{\overline{24}|0.0075}=21,889.15 \\ & 21,889.15=2000 a_{\overline{n}| 0.0075} \\ & n=11.46 \end{aligned} [[/math]]

Drop payment will be made at the [math]12^{\text {th }}[/math] month.

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