A payday loan company charges a $40 fee for a $500 payday loan that will be repaid in 20 days.

Treating the fee as interest paid, what is the equivalent annual interest rate?

To calculate the equivalent annual interest rate (APR) for the payday loan, we can use the formula for simple interest, adjusted for the time period:

\[
\text{APR} = \left( \frac{\text{Interest}}{\text{Loan Amount}} \right) \times \frac{365}{\text{Loan Term in Days}} \times 100
\]

### Step-by-step calculation:

1. **Interest Paid:** 
   - The fee is $40, which is treated as the interest.

2. **Loan Amount:** 
   - The loan amount is $500.

3. **Loan Term:** 
   - The loan term is 20 days.

4. **Substitute values into the formula:**

\[
\text{APR} = \left( \frac{40}{500} \right) \times \frac{365}{20} \times 100
\]

\[
\text{APR} = 0.08 \times 18.25 \times 100
\]

\[
\text{APR} = 146%
\]

### Final Result:
The equivalent annual interest rate (APR) for this payday loan is approximately **146%**.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How does the APR compare to other types of loans, like credit cards or mortgages?
2. What are the risks of payday loans at such high interest rates?
3. How can you calculate the effective interest rate for loans with varying repayment terms?
4. How would the APR change if the loan period was longer or shorter?
5. What are alternative loan options with lower interest rates?

**Tip:** Always check the APR when considering short-term loans, as high fees over short periods can lead to significantly higher annualized costs.

A payday loan company charges a $40 fee for a $500 payday loan that will be repaid in 20 days. Treating the fee as interest paid, what is the equivalent annual interest rate?

Find out how to calculate the equivalent annual interest rate (APR) for a payday loan with a $40 fee on a $500 loan that will be repaid in 20 days. This detailed step-by-step solution uses simple interest formulas to determine an APR of approximately 146%. Suitable for students in Grades 10-12 and anyone exploring loan interest calculations.

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