A payday loan company charges a $55 Fee for a $650 payday loan that will be paid in 13 days treating the fee is interest paid, what is the equivalent annual interest rate?

To determine the equivalent annual interest rate for the payday loan, we need to follow a step-by-step process. Here's how to do it:

1. **Identify given values**:
   - Loan amount: $ P = 650 $ (principal)
   - Fee (interest): $ I = 55 $
   - Loan period: $ t = 13 $ days

2. **Calculate the interest rate for the 13-day period**:
   The interest rate for the 13 days is the fee divided by the loan amount:
   \[
   r_{13} = \frac{I}{P} = \frac{55}{650} = 0.0846
   \]
   This is the interest rate for the 13-day period (about 8.46%).

3. **Convert the 13-day interest rate to an annual interest rate**:
   Since there are $ \frac{365}{13} $ periods like this in a year, the annual interest rate is calculated by multiplying the 13-day rate by the number of such periods in a year:
   \[
   r_{\text{annual}} = r_{13} \times \frac{365}{13}
   \]
   Let's calculate this.

I'll compute the final value now.The equivalent annual interest rate for the payday loan is approximately **237.57%**.

Would you like more details on how this was calculated or any clarifications?

Here are 5 related questions you might find useful:
1. How does the duration of a loan affect its interest rate?
2. What is the difference between simple interest and compound interest?
3. How would the interest change if the loan was repaid in 30 days instead?
4. What is the typical range for annual interest rates on payday loans?
5. How do payday loans compare to traditional bank loans in terms of interest rates?

**Tip:** Payday loans tend to have extremely high annual interest rates due to their short repayment periods, making them a costly borrowing option. Always consider the full cost before taking one out.

A payday loan company charges a $55 Fee for a $650 payday loan that will be paid in 13 days treating the fee as interest paid, what is the equivalent annual interest rate?

Discover how to calculate the equivalent annual interest rate for a payday loan of $650 with a $55 fee over 13 days. This example covers key financial concepts like interest rate calculation and annualization. Ideal for high school students in Grades 10-12.

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