Credit Card Payment Calculator

What is a Credit Card Payment Calculator?

A Credit Card Payment Calculator is a financial tool that helps you determine how long it will take to pay off your credit card balance and how much interest you'll pay over that time. It takes into account your current balance, the card's annual percentage rate (APR), and your monthly payment to provide a clear picture of your debt repayment journey.

The Formula

The calculator uses the following formula to determine the number of months needed to pay off your credit card balance:

\[ N = -\frac{\log(1 - \frac{i \cdot B}{P})}{\log(1 + i)} \]

Where:

• \(N\) = Number of months to pay off the balance
• \(i\) = Monthly interest rate (APR / 12 / 100)
• \(B\) = Current credit card balance
• \(P\) = Monthly payment amount

Calculation Steps

To use the Credit Card Payment Calculator, follow these steps:

1. Input your current credit card balance (\(B\))
2. Enter the card's Annual Percentage Rate (APR)
3. Specify your intended monthly payment (\(P\))
4. Calculate the monthly interest rate: \(i = \frac{APR}{12 \times 100}\)
5. Apply the formula: \(N = -\frac{\log(1 - \frac{i \cdot B}{P})}{\log(1 + i)}\)
6. Round up \(N\) to the nearest whole number to get the number of months
7. Calculate total amount paid: Total = \(P \times N\)
8. Calculate total interest paid: Interest = Total - \(B\)

Example and Visual Representation

Let's work through an example:

• Current Balance (\(B\)): $5,000
• APR: 18%
• Monthly Payment (\(P\)): $200

1. Calculate monthly interest rate: \[ i = \frac{18}{12 \times 100} = 0.015 \]
2. Apply the formula: \[ N = -\frac{\log(1 - \frac{0.015 \times 5000}{200})}{\log(1 + 0.015)} \approx 32.6 \text{ months} \]
3. Round up to 33 months
4. Calculate total paid: \[ \text{Total} = 200 \times 33 = $6,600 \]
5. Calculate total interest: \[ \text{Interest} = 6,600 - 5,000 = $1,600 \]

Visual representation of the payoff:

This visual representation illustrates:

• The total amount paid ($6,600) shown by the entire bar
• The principal amount ($5,000) in green
• The interest paid ($1,600) in blue
• The time required to pay off the balance (33 months)

By using this Credit Card Payment Calculator, you can make informed decisions about your debt repayment strategy and understand the long-term impact of your monthly payments on your credit card balance.