Question
You owe $1,240.24 on a credit card with a 23.75% APR. You decide to pay $250.00/month toward paying off the credit card. How much is the difference in the interest paid after one month if you pay at the beginning of the month compared to paying at the end of the month?
Answers
GPT-4o mini
To calculate the difference in interest paid after one month when paying at the beginning of the month versus at the end of the month, we first need to determine the interest charges for each scenario.
1. **Calculate Monthly Interest Rate:**
The annual percentage rate (APR) is 23.75%. To find the monthly interest rate, we divide the APR by 12 months:
\[
\text{Monthly Interest Rate} = \frac{23.75\%}{12} = \frac{0.2375}{12} \approx 0.0197917
\]
2. **Scenario 1: Payment at the Beginning of the Month**
- Current balance: $1,240.24
- Payment amount: $250.00
- Remaining balance after payment:
\[
\text{New Balance} = 1240.24 - 250.00 = 990.24
\]
- Interest charged based on the original balance before payment:
\[
\text{Interest} = 1240.24 \times 0.0197917 \approx 24.54
\]
- Total amount due at the end of the month:
\[
\text{Total Due} = \text{New Balance} + \text{Interest} = 990.24 + 24.54 \approx 1014.78
\]
3. **Scenario 2: Payment at the End of the Month**
- Interest is calculated based on the original balance for the entire month before the payment is made. The interest charged:
\[
\text{Interest} = 1240.24 \times 0.0197917 \approx 24.54 \text{ (same as above)}
\]
- New balance after adding interest before payment:
\[
\text{New Balance After Interest} = 1240.24 + 24.54 = 1264.78
\]
- Remaining balance after making the payment at the end of the month:
\[
\text{Remaining Balance} = 1264.78 - 250.00 = 1014.78
\]
4. **Calculate the Difference in Interest Paid:**
- In both scenarios, the interest charged is approximately $24.54, and therefore, the total remaining balances after one month are the same in this case.
Thus, the difference in the interest paid after one month if you pay at the beginning of the month compared to paying at the end of the month is **$0**.
1. **Calculate Monthly Interest Rate:**
The annual percentage rate (APR) is 23.75%. To find the monthly interest rate, we divide the APR by 12 months:
\[
\text{Monthly Interest Rate} = \frac{23.75\%}{12} = \frac{0.2375}{12} \approx 0.0197917
\]
2. **Scenario 1: Payment at the Beginning of the Month**
- Current balance: $1,240.24
- Payment amount: $250.00
- Remaining balance after payment:
\[
\text{New Balance} = 1240.24 - 250.00 = 990.24
\]
- Interest charged based on the original balance before payment:
\[
\text{Interest} = 1240.24 \times 0.0197917 \approx 24.54
\]
- Total amount due at the end of the month:
\[
\text{Total Due} = \text{New Balance} + \text{Interest} = 990.24 + 24.54 \approx 1014.78
\]
3. **Scenario 2: Payment at the End of the Month**
- Interest is calculated based on the original balance for the entire month before the payment is made. The interest charged:
\[
\text{Interest} = 1240.24 \times 0.0197917 \approx 24.54 \text{ (same as above)}
\]
- New balance after adding interest before payment:
\[
\text{New Balance After Interest} = 1240.24 + 24.54 = 1264.78
\]
- Remaining balance after making the payment at the end of the month:
\[
\text{Remaining Balance} = 1264.78 - 250.00 = 1014.78
\]
4. **Calculate the Difference in Interest Paid:**
- In both scenarios, the interest charged is approximately $24.54, and therefore, the total remaining balances after one month are the same in this case.
Thus, the difference in the interest paid after one month if you pay at the beginning of the month compared to paying at the end of the month is **$0**.