A borrower takes out a 15-year loan for 65,000, with level end-of-month payments. The annual nominal interest rate of the loan is 8%, convertible monthly. Immediately after the 12th payment is made, the remaining loan balance is reamortized. The maturity date of the loan remains unchanged, but the annual nominal interest rate of the loan is changed to 6%, convertible monthly.

Calculate the new end-of-month payment.

• 528
• 534
• 540
• 546
• 552

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

Solution: E

The monthly payment on the original loan is

[[math]]\frac{65000}{a_{\overline{180}|8/12 \%}}=621.17.[[/math]]

After 12 payments the outstanding balance is

[[math]]621.17a_{\overline{168}|8/12 \%}=62,661.40[[/math]]

. The revised payment is

[[math]]\frac{62,661.40}{a_{\overline{168}|6/12\%}}=552.19. [[/math]]

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