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To solve this question, we need to calculate the Annual Percentage Rate (APR) for the loan. The problem provides the following details:

- Loan amount: $500
- Interest rate: $20 per $100 borrowed
- Loan duration: 4 weeks

### Step 1: Calculate the Interest Rate for 4 weeks
Since the interest is $20 per $100 borrowed, the interest on $500 would be:
\[
\text{Interest} = \left(\frac{20}{100}\right) \times 500 = 100 \, \text{dollars}
\]
This is the interest you would pay for borrowing $500 for 4 weeks.

### Step 2: Convert to APR (Annual Percentage Rate)
The APR reflects the annualized interest rate. Since this loan is for 4 weeks, we need to convert it to an annual rate. There are 52 weeks in a year, so:
\[
\text{Number of periods in a year} = \frac{52}{4} = 13
\]

Now, multiply the interest rate by 13 to annualize it:
\[
\text{APR} = 100 \times 13 = 1300 \, \text{dollars in interest annually on a } 500 \, \text{loan}
\]

To express this as a percentage of the loan:
\[
\text{APR percentage} = \left(\frac{1300}{500}\right) \times 100 = 260\%
\]

So, the APR is **260%**.

Let me know if you need more details or have questions. Here are some related questions to consider:

1. How is APR different from simple interest?
2. What is the effective interest rate if compounding occurs weekly?
3. How would the APR change if the loan duration was 8 weeks?
4. Can the interest rate be calculated differently for varying loan amounts?
5. What happens if additional fees are added to the loan?

**Tip:** Always double-check the time period when converting interest rates to an annual rate!

Suppose you wish to borrow $500 for four weeks and the amount of interest you must pay is $20 per $100 borrowed. What is the APR at which you are borrowing money?

Learn how to calculate the Annual Percentage Rate (APR) for a $500 loan, where the interest is $20 per $100 borrowed for a 4-week period. This involves simple interest and proportion calculations. Suitable for students in Grades 9-12.

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