A payday loan company charges a 560 fee for a $650 payday loan that will be repaid in 14 days. Treating the fee as interest paid, what is the equivalent annual interest rate? % interest Round to the nearest percent. This will be over 100%

To calculate the equivalent annual interest rate (APR) for the payday loan, we follow these steps:

1. **Calculate the interest amount**:  
   The fee is treated as the interest, so:
   \[
   \text{Interest} = 560 \text{ dollars}
   \]

2. **Find the interest rate for 14 days**:  
   The interest rate for 14 days is the interest amount divided by the loan amount:
   \[
   \text{Interest rate for 14 days} = \frac{560}{650} \approx 0.8615
   \]
   This represents 86.15% over 14 days.

3. **Annualize the interest rate**:  
   Since the loan period is 14 days, we need to find how many 14-day periods there are in a year:
   \[
   \text{Number of 14-day periods in a year} = \frac{365}{14} \approx 26.07
   \]
   To find the equivalent annual interest rate, multiply the 14-day interest rate by the number of periods in a year:
   \[
   \text{Annual interest rate} = 0.8615 \times 26.07 \approx 22.45
   \]
   Therefore, the equivalent annual interest rate (APR) is approximately:
   \[
   \text{APR} \approx 2245\%
   \]

### Final Answer:
The equivalent annual interest rate is approximately **2245%**.

Would you like more details or have any questions?

### 5 Related Questions:
1. How does APR differ from simple interest?
2. What is the formula for calculating APR on different loan periods?
3. Why is the interest rate for payday loans typically so high?
4. How can compounding affect the equivalent annual interest rate?
5. What alternatives are there to payday loans with lower APRs?

### Tip:
Payday loans often have extremely high APRs, so it’s helpful to explore alternatives like credit unions or personal installment loans to avoid excessive interest.

A payday loan company charges a 560 fee for a $650 payday loan that will be repaid in 14 days. Treating the fee as interest paid, what is the equivalent annual interest rate? % interest Round to the nearest percent. This will be over 100%.

Learn how to calculate the equivalent annual interest rate (APR) for a payday loan with a $560 fee on a $650 loan, repaid in 14 days. This problem covers interest rate calculation, proportional scaling, and APR formula. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation