Revision as of 23:59, 18 November 2023 by Admin (Created page with "A small business takes out a 10-year loan with level end-of-quarter payments. The payments are based on an annual nominal interest rate of 12% convertible quarterly. The amount of principal repaid in the 15th payment is 10,030.27. Calculate the amount of interest paid in the 25th payment. <ul class="mw-excansopts"><li>7,521</li><li>8,151</li><li>9,467</li><li>10,030</li><li>11,601</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
A small business takes out a 10-year loan with level end-of-quarter payments. The payments are based on an annual nominal interest rate of 12% convertible quarterly. The amount of principal repaid in the 15th payment is 10,030.27.
Calculate the amount of interest paid in the 25th payment.
- 7,521
- 8,151
- 9,467
- 10,030
- 11,601
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: B
The amount of principal repaid at payment 15 is (where R is the quarterly payment)
[[math]]
10.030.27=R v^{0.13+1}=R(1.03)^{-26}\Rightarrow R=10.030.27(1.03)^{26}=21.631.19.
[[/math]]
The amount of interest in payment 25 is
[[math]]
21,631.19(1-{ v}^{40-25+1})=21,631.19(1-1.03^{-16})=8,151.35.
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.