A payday loan company charges a $75 fee for a $450 payday loan that will be repaid in 11 days.

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

To calculate the equivalent annual interest rate, we first need to find the interest rate for the 11-day period, and then convert that to an annual rate.

### Step 1: Calculate the interest rate for 11 days

The loan amount is $450, and the fee is $75. The interest rate for the 11-day period can be calculated as:

\[
\text{Interest rate for 11 days} = \frac{\text{Fee}}{\text{Loan amount}} = \frac{75}{450} = 0.1667
\]

This means the interest rate for the 11 days is 16.67%.

### Step 2: Convert to an annual interest rate

There are 365 days in a year, so the number of 11-day periods in a year is:

\[
\text{Number of 11-day periods in a year} = \frac{365}{11} \approx 33.18
\]

Now, to find the annual interest rate, we multiply the interest rate for 11 days by the number of 11-day periods in a year:

\[
\text{Annual interest rate} = 0.1667 \times 33.18 \approx 5.53
\]

So the equivalent annual interest rate is approximately **553%**.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How does compound interest affect payday loans compared to simple interest?
2. What is the impact of short-term loans on a borrower's credit score?
3. How do payday loan fees compare to other forms of short-term credit, such as credit cards?
4. How does the annual percentage rate (APR) differ from the nominal interest rate?
5. What are some common alternatives to payday loans for short-term financial needs?

**Tip:** Always calculate the effective interest rate when comparing loans with different repayment periods.

A payday loan company charges a $75 fee for a $450 payday loan that will be repaid in 11 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 $75 fee on a $450 loan repaid in 11 days. Understand key concepts like the interest rate for a period and how to annualize short-term interest rates. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation