A borrower planned to repay a loan of L with level payments at the end of each month for 30 years. The loan had an annual nominal interest rate of 6%, convertible monthly. Starting with the 181st payment, the borrower increased the monthly payment to 2000, which enabled the borrower to pay off the loan five years earlier than planned.

Calculate L.

• 253,554
• 277,772
• 310,414
• 330,347
• 333,583

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

Solution: A

[[math]] \begin{aligned} & O B_{180}=2000 a_{\left.\overline{120}\right|0.005}=180,146.91 \\ & 180,146.91=P a_{\overline{180} \mid 0.005} \\ & P=1520.18 \\ & L=1520.18 a_{\overline{360}|_{0.005}}=253,553.61\end{aligned} [[/math]]

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