A loan with an annual nominal interest rate of 9%, convertible monthly, is repaid with 60 monthly payments. The first payment is 1000 and each succeeding payment is 2% less than the previous payment.

Calculate the outstanding loan balance immediately after the 40 th payment is made

• 6889
• 7289
• 7344
• 7407
• 7862

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

Solution: A

The outstanding loan balance at any point in time is equal to the present value (at that same point in time) of the remaining installment payments.

[[math]] B_{40}=1000(0.98)^{40}\left[\frac{1-\left(\frac{0.98}{1.0075}\right)^{20}}{0.0075+0.02}\right]=6889.11 [[/math]]

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