A payday loan company charges a $90 fee for a $500 payday loan that will be repaid in 14 days.

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

To find the equivalent annual interest rate for a payday loan, we need to first calculate the simple interest rate over the 14-day period and then annualize it.

The formula for simple interest is:

\[
\text{Interest rate} = \frac{I}{P \times t}
\]

Where:
- $ I $ is the interest (in this case, the fee of $90),
- $ P $ is the principal (the loan amount of $500),
- $ t $ is the time period in years.

### Step 1: Calculate the interest rate for the 14-day period
Here, $ t $ is $ \frac{14}{365} $ because 14 days is part of a year.

\[
\text{Interest rate for 14 days} = \frac{90}{500 \times \frac{14}{365}} = \frac{90}{500} \times \frac{365}{14}
\]

Now let's calculate that:

\[
\text{Interest rate for 14 days} = \frac{90}{500} \times \frac{365}{14} = 0.18 \times 26.07 \approx 4.6926
\]

So, the interest rate for the 14-day period is approximately 4.6926, or 469.26%.

### Step 2: Convert to an annual interest rate
Since this interest rate is for a 14-day period, the equivalent annual interest rate (APR) is already calculated, as the interest rate for a 14-day period is multiplied by 26.07 (the number of 14-day periods in a year).

Thus, the equivalent annual interest rate is **469.26%**.

Would you like further details or clarification?

Here are 5 related questions to expand your understanding:
1. How is simple interest different from compound interest?
2. What would the interest rate be for a different loan period (e.g., 30 days)?
3. How would this interest rate affect the total repayment over multiple loans?
4. How can payday loans lead to debt cycles for borrowers?
5. What is the typical interest rate on other types of loans, such as personal loans or credit cards?

**Tip:** Payday loans often carry very high interest rates due to their short terms, so it's important to compare their costs with other borrowing options.

A payday loan company charges a $90 fee for a $500 payday loan that will be repaid in 14 days. Treating the fee as simple interest paid, what is the equivalent annual interest rate?

Learn how to calculate the equivalent annual interest rate for a payday loan with a $90 fee on a $500 loan repaid in 14 days. This problem explores simple interest concepts and shows how to annualize short-term interest rates. Suitable for Grades 9-12 students and beyond.

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