Credit Card Interest Calculator

What is Credit Card Interest?

Credit card interest is the cost of borrowing money on your credit card. It's typically expressed as an Annual Percentage Rate (APR) and is charged when you carry a balance from month to month. Understanding how credit card interest works is crucial for managing your finances and avoiding excessive debt.

Formula for Credit Card Interest Calculation

The formula to calculate the number of months needed to pay off a credit card balance is:

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

Where:

• \(N\) is the number of months to pay off the balance
• \(P\) is the monthly payment
• \(B\) is the initial balance
• \(r\) is the monthly interest rate (APR / 12 / 100)

Calculation Steps

To calculate the time needed to pay off your credit card and the total interest paid, follow these steps:

1. Calculate the monthly interest rate by dividing the APR by 12 and 100
2. Use the formula to calculate the number of months needed to pay off the balance
3. Calculate the total amount paid by multiplying the monthly payment by the number of months
4. Calculate the total interest paid by subtracting the initial balance from the total amount paid

Example and Visual Representation

Let's calculate the payoff time and interest for a credit card balance:

• Initial Balance: $5,000
• APR: 18%
• Monthly Payment: $200

1. Calculate monthly interest rate: \[ r = \frac{18}{12 * 100} = 0.015 \]
2. Calculate months to pay off: \[ N = \frac{\log(\frac{200}{200 - 5000 * 0.015})}{\log(1 + 0.015)} \approx 32.6 \text{ months} \]
3. Calculate total paid: \[ \text{Total Paid} = 200 * 32.6 \approx $6,520 \]
4. Calculate total interest: \[ \text{Total Interest} = 6,520 - 5,000 = $1,520 \]

Visual representation of the payoff:

This visual representation shows:

• The total amount paid ($6,520) represented by the entire bar
• The principal amount ($5,000) in green
• The interest paid ($1,520) in blue
• The time taken to pay off the balance (32.6 months)