To determine how long it will take to pay off the credit card balance and the total interest paid, we can use the following formula for monthly payments on a credit card:
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Calculate the monthly interest rate: \[ \text{Monthly interest rate} = \frac{\text{Annual interest rate}}{12} = \frac{11.3%}{12} = \frac{0.113}{12} \approx 0.00942 \]
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Use the balance, payment, and interest rate to set up an amortization equation. The remaining balance after each payment will be calculated as follows: \[ \text{New Balance} = \text{Old Balance} \times (1 + \text{Monthly interest rate}) - \text{Payment} \]
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Begin with the initial balance of $1,568.00 and subtract $300 monthly until it is paid off while adding interest.
Calculation:
Initial Balance = $1,568.00
Monthly Payment = $300.00
Monthly Interest Rate = 0.00942
Let's outline the monthly calculations to see how many months it will take to pay it off. We'll go through the iteration month-by-month:
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Month 1: \[ \text{New Balance} = 1568 \times (1 + 0.00942) - 300 \approx 1568 \times 1.00942 - 300 \approx 1268.36 \]
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Month 2: \[ \text{New Balance} = 1268.36 \times 1.00942 - 300 \approx 1268.36 \times 1.00942 - 300 \approx 973.96 \]
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Month 3: \[ \text{New Balance} = 973.96 \times 1.00942 - 300 \approx 973.96 \times 1.00942 - 300 \approx 674.39 \]
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Month 4: \[ \text{New Balance} = 674.39 \times 1.00942 - 300 \approx 674.39 \times 1.00942 - 300 \approx 376.51 \]
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Month 5: \[ \text{New Balance} = 376.51 \times 1.00942 - 300 \approx 376.51 \times 1.00942 - 300 \approx 78.31 \]
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Month 6: \[ \text{New Balance} = 78.31 \times 1.00942 - 300 \approx 78.31 \times 1.00942 - 300 \approx -220.4 \]
This shows that in Month 6, the remaining balance goes negative, indicating you fully pay off the debt during that payment.
Summary:
It takes 6 months to pay off the credit card debt.
Total Interest Paid Calculation:
To calculate total interest paid:
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Calculate the total amount paid: \[ \text{Total Paid} = \text{Monthly Payment} \times \text{Months Paid} = 300 \times 6 = 1,800 \]
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Subtract the original balance from the total paid to find total interest: \[ \text{Total Interest Paid} = \text{Total Paid} - \text{Initial Balance} = 1,800 - 1,568 = 232 \]
Results:
- Number of months to pay off: 6 months
- Total interest paid: $232.00