A loan of 100,000 at an annual effective rate of 9.12% is repaid with level payments at the end of each month over 15 years. Immediately after the 59th payment is made, the outstanding balance is refinanced at an annual effective rate of 5.76%. The term of the refinanced loan is 20 years with level payments at the end of each month.

Calculate the interest portion of the first payment of the refinanced loan.

• 375
• 378
• 381
• 384
• 387

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

Solution: A

[[math]] \begin{aligned} & 1.0912=(1+j)^{12} \\ & j=0.0073 \\ & 100,000=P a_{\overline{180} | 0.0073} \\ & P=1000.02 \\ & O B_{59}=1000.02 a_{\overline{1210} | 0.0073} \\ & O B_{59}=80,174.59 \\ & 1.0576=(1+j)^{12} \\ & j=0.004678 \end{aligned} [[/math]]

Interest portion of first revised payment:

[[math]] 80,174.59(0.004678)=375.04 \text {. } [[/math]]

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