Revision as of 13:27, 19 November 2023 by Admin (Created page with "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 <ul class="mw-excansopts"><li>6889</li><li>7289</li><li>7344</li><li>7407</li><li>7862</li></ul> {{soacopyright | 2023 }}")
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.