A payday loan company charges a $25 fee for a $450 payday loan that will be repaid in 16 days.
Treating the fee as interest paid, what is the equivalent annual interest rate?

To calculate the equivalent annual interest rate for the payday loan, we can use the formula for **simple interest**. In this case, we need to find the interest rate that corresponds to the $25 fee charged for a 16-day loan of $450.

Here are the steps:

### 1. **Calculate the interest rate for the loan period:**

The interest rate for the loan period is the ratio of the fee to the loan amount. Thus, for the 16-day loan:

\[
\text{Interest rate for 16 days} = \frac{\text{Fee}}{\text{Loan amount}} = \frac{25}{450}
\]

\[
\text{Interest rate for 16 days} = 0.05556 \text{ or } 5.56\%
\]

### 2. **Annualize the interest rate:**

To convert this to an annual interest rate, we need to scale it up from the 16-day period to a full year (365 days). We can do this by dividing the number of days in a year by the number of days in the loan period and multiplying by the interest rate:

\[
\text{Annual interest rate} = \left( \frac{365}{16} \right) \times 0.05556
\]

### 3. **Perform the calculation:**

\[
\text{Annual interest rate} = 22.8125 \times 0.05556 = 1.2673 \text{ or } 126.73\%
\]

### Conclusion:

The equivalent annual interest rate for the payday loan is approximately **126.73%**.

Would you like further details or have any questions? Here are some related questions you might find helpful:

1. How is simple interest different from compound interest?
2. What would the annual interest rate be for different loan periods, like 30 days?
3. How does a payday loan's APR compare to a standard credit card APR?
4. Can you calculate the monthly equivalent interest rate from the annual rate?
5. What risks are associated with payday loans due to their high-interest rates?

**Tip:** Payday loans often have very high annual interest rates, so it's important to compare their cost to other borrowing options.

A payday loan company charges a $25 fee for a $450 payday loan that will be repaid in 16 days. Treating the fee as interest paid, what is the equivalent annual interest rate?

Learn how to calculate the equivalent annual interest rate for a payday loan with a $25 fee on a $450 loan over 16 days. This problem covers concepts of simple interest and how to annualize interest rates. Suitable for high school students in Grades 10-12.

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