Tanner takes out a loan today and repays the loan with eight level annual payments, with the first payment one year from today. The payments are calculated based on an annual effective interest rate of 4.75%. The principal portion of the fifth payment is 699.68.

Calculate the total amount of interest paid on this loan.

• 1239
• 1647
• 1820
• 2319
• 2924

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

Solution: A

[[math]] \begin{align*} 699.68=P\nu^{8-5+1}\\ P=842.39~(\textrm{annual payment})\\ P_{1}=\frac{609.68}{1.0475^{4}}=581.14 \\ I_{1}=842.39-581.14=261.25 \\ L =\frac{261.25}{0.0475}=5500 (\textrm{loan amount}) \end{align*} [[/math]]

Total interest = 842.39(8) - 5500 = 1239.12.

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