Questions: A payday loan company charges a 90 fee for a 400 payday loan that will be repaid in 15 days. Treating the fee as interest paid, what is the equivalent annual interest rate? % interest

Solution Steps

The interest rate for the loan period is calculated as follows:

\[ \text{Interest Rate for Loan Period} = \frac{\text{Fee}}{\text{Loan Amount}} = \frac{90}{400} = 0.225 \]

To find the daily interest rate, we divide the interest rate for the loan period by the number of days in the loan period:

\[ \text{Daily Interest Rate} = \frac{\text{Interest Rate for Loan Period}}{\text{Loan Period Days}} = \frac{0.225}{15} = 0.015 \]

Next, we scale the daily interest rate to an annual interest rate by multiplying by the number of days in a year:

\[ \text{Annual Interest Rate} = \text{Daily Interest Rate} \times \text{Days in Year} = 0.015 \times 365 = 5.475 \]

Finally, we convert the annual interest rate to a percentage:

\[ \text{Annual Interest Rate Percentage} = \text{Annual Interest Rate} \times 100 = 5.475 \times 100 = 547.5 \]

Final Answer