5000 is borrowed at an annual nominal rate of interest of j convertible monthly. The loan is repaid with payments of 291.23 at the end of each quarter for 5 years.

Calculate j.

• 5.97%
• 6.00%
• 6.04%
• 6.09%
• 6.14%

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

Solution: A

Define [math]i^{\prime}[/math] as the quarterly effective interest rate for the loan Solve for [math]i^{\prime}[/math]

[[math]] \begin{aligned} & 291.23 a_{\overline{20} \mid i^{\prime}}=5000 \\ & i^{\prime}=1.5 \% \end{aligned} [[/math]]

Then, solve for [math]j[/math] using the formula

[[math]] \begin{aligned} & \left(1+\frac{j}{12}\right)^{12}=(1+0.015)^4 \\ & j=0.0597 \end{aligned} [[/math]]

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