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ABy Admin
Nov 19'23
Exercise
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.
ABy Admin
Nov 19'23
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.