Question

You owe $1,568.00 on a credit card with a limit of $2,200.00 at an interest rate of 11.3%. You pay $300/month until it is paid off.
How many months does it take you to pay it off and how much is the total interest paid?

Answer 1

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:

1. Calculate the monthly interest rate:
\[
\text{Monthly interest rate} = \frac{\text{Annual interest rate}}{12} = \frac{11.3\%}{12} = \frac{0.113}{12} \approx 0.00942
\]

2. Use the balance, payment, and interest rate to set up an amortization equation. The remaining balance after each payment will be calculated as follows:
\[
\text{New Balance} = \text{Old Balance} \times (1 + \text{Monthly interest rate}) - \text{Payment}
\]

3. 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:

- **Month 1:**
\[
\text{New Balance} = 1568 \times (1 + 0.00942) - 300 \approx 1568 \times 1.00942 - 300 \approx 1268.36
\]

- **Month 2:**
\[
\text{New Balance} = 1268.36 \times 1.00942 - 300 \approx 1268.36 \times 1.00942 - 300 \approx 973.96
\]

- **Month 3:**
\[
\text{New Balance} = 973.96 \times 1.00942 - 300 \approx 973.96 \times 1.00942 - 300 \approx 674.39
\]

- **Month 4:**
\[
\text{New Balance} = 674.39 \times 1.00942 - 300 \approx 674.39 \times 1.00942 - 300 \approx 376.51
\]

- **Month 5:**
\[
\text{New Balance} = 376.51 \times 1.00942 - 300 \approx 376.51 \times 1.00942 - 300 \approx 78.31
\]

- **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:

1. Calculate the total amount paid:
\[
\text{Total Paid} = \text{Monthly Payment} \times \text{Months Paid} = 300 \times 6 = 1,800
\]

2. 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**