A bank offers a loan to each of two borrowers with different credit scores. Both loans are for the same amount. The first borrower is charged a monthly effective interest rate of 1% and makes level end-of- month payments of X for n months to pay off the loan. The second borrower is charged a monthly effective interest rate of 2.01% and makes level end- of-month payments of 2.01X for 200 months to pay off the loan.

Calculate n.

• 200
• 250
• 300
• 350
• 400

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

Solution: E

[[math]] \begin{aligned} & X a_{\overline{n}| 0.01}=2.01 X a_{\overline{200} \mid 0.0201} \\ & a_{\overline{n} |0.01}=2.01 a_{\overline{200}|0.0201} \\ & a_{\overline{n}| 0.01}=98.13168 \\ & n=400 \end{aligned} [[/math]]

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