On the first of the month, Chuck took out a business loan for 50,000, with payments at the end of each month based on an annual nominal interest rate compounded monthly. Each monthly payment is equal to 800, except for a final drop payment. Immediately after the first payment the balance owed was 49,800.

Calculate the number of payments that Chuck needed to pay off the loan.

• 115
• 117
• 119
• 121
• 123

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

Solution: B

Let [math]j[/math] be the monthly interest rate.

[[math]] \begin{aligned} & 50,000(1+j)-800=49,800 \\ & j=0.012 \\ & 50,000=800 a_{n \mid 0.012} \\ & n=116.22 \end{aligned} [[/math]]

Drop payment at payment number 117.

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