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.

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.