Questions: Suppose you wish to borrow 600 for four weeks and the amount of interest you must pay is 25 per 100 borrowed. What is the APR at which you are borrowing money?

Solution Steps

To find the total interest for the loan, we scale the interest amount per $100 to the total loan amount. This is calculated as \((L / 100) \times I_{100}\), where \(L\) is the loan amount ($600) and \(I_{100}\) is the interest amount per $100 ($25). Thus, the total interest for the loan duration is $150.

Since the interest rate is given for a period shorter than a year, we convert it to an annual rate. The factor to annualize the interest rate is \(52 / D_w\), where \(D_w\) is the loan duration in weeks (4 weeks). Therefore, the annualization factor is 13.

The APR is calculated by multiplying the interest rate for the loan duration by the annualization factor. The formula for APR is thus \(\left(\frac{I_{100}}{100} \times \frac{52}{D_w}\right) \times 100\% = \left(\frac{I_{100}}{100} \times \frac{52}{4}\right) \times 100\% = 325\%\).

Final Answer: The APR for the loan is 325%.