Question

If you borrow \(5,300 at \)400 interest for one year, what is your effective interest rate for the following payment plans?

c. Quarterly payments.

Short answer

The effective interest rate is 12.07%.

Step-by-step solution

Information provided in the question

Loan amount = $5,300

Loan term = 1 year

Interest = $400

Number of payments = 4

Calculation of effective interest rate on the instalment loan

The effective interest rate on an instalment loan is 12.07%.

$\begin{array}{rcl}\mathrm{Effective}\mathrm{rate}& =& \frac{2\times \mathrm{Annual}\mathrm{number}\mathrm{of}\mathrm{payments}\times \mathrm{Interest}}{\left(\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{payments}+1\right)\times \mathrm{Principal}}\\ & =& \frac{2\times 4\times \$400}{\left(4+1\right)\times \$5,300}\\ & =& \frac{\$3,200}{\$26,500}\\ & =& 12.07\%\end{array}$