Garth had unexpected expenses this month and didn’t have enough in his savings account to pay the rent of $600. He went to Loanshark Larry’s to borrow the money until his next paycheck 15 days from now. Larry charges $100 interest for the 15 days. What is the APR for his payday loan? Round to the nearest whole percent. Use the payday APR formula: APR=loan interest/loan amount divided by loan length in days/365) times 100

To calculate the Annual Percentage Rate (APR) using the payday loan formula, let's break down the steps.

Given:
- Loan amount = $600
- Loan interest = $100
- Loan length = 15 days
- The formula for APR is:
\[
APR = \left( \frac{\text{Loan Interest}}{\text{Loan Amount}} \div \frac{\text{Loan Length in Days}}{365} \right) \times 100
\]

### Step 1: Calculate the fraction of the year for 15 days
\[
\frac{15}{365} \approx 0.0411
\]

### Step 2: Calculate the loan interest over the loan amount
\[
\frac{100}{600} = 0.1667
\]

### Step 3: Divide the result of step 2 by the fraction of the year (from step 1)
\[
\frac{0.1667}{0.0411} \approx 4.054
\]

### Step 4: Multiply by 100 to get the APR
\[
APR = 4.054 \times 100 \approx 405.4\%
\]

### Rounded to the nearest whole percent:
\[
APR \approx 405\%
\]

So, the APR for Garth's payday loan is approximately **405%**.

Would you like further details or clarifications on this?

Here are 5 related questions to explore further:
1. How is APR different from other types of interest rates?
2. What is the significance of compounding in APR calculations?
3. How would the APR change if the loan length were longer?
4. What are some potential dangers of payday loans with high APRs?
5. How does APR compare to simple interest?

**Tip:** Payday loans often have very high APRs due to their short loan duration and fixed interest, making them expensive if not paid off quickly.

Garth had unexpected expenses this month and didn’t have enough in his savings account to pay the rent of $600. He went to Loanshark Larry’s to borrow the money until his next paycheck 15 days from now. Larry charges $100 interest for the 15 days. What is the APR for his payday loan? Round to the nearest whole percent. Use the payday APR formula: APR = (loan interest/loan amount) ÷ (loan length in days/365) × 100.

Learn how to calculate the APR for a payday loan with a $100 interest on a $600 loan, borrowed for 15 days. Using the APR formula, follow a detailed step-by-step breakdown, ideal for students in Grades 9-12 or those interested in personal finance calculations.

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