A homeowner borrows 1000 to be repaid with payments at the end of each year for 20 years. There are two repayment options. The first option is equal annual payments based on an annual effective interest rate of 3%. The second option is payments of 50 each year plus interest on the unpaid balance at an annual effective interest rate of i. The total payments under the two options are the same.

Calculate i.

• 2.86%
• 3.00%
• 3.28%
• 3.44%
• 4.76%

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

Solution: C

[[math]] \begin{aligned} & 1000=P a_{\overline{20}|0.03} \\ & P=67.22 \\ & 67.22(20)=1344.31 \\ & 1344.31=1000+i(1000+950+900+\cdots+50) \\ & 344.31=i(10,500) \\ & i=0.03279\end{aligned} [[/math]]

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