Credit card payoff calculator
Card interest compounds monthly on the balance. A fixed payment clears it in a number of months you can solve for directly.
%
Months to clear
34.3
- Years
- 2.86
- Total interest
- 1859.39
- Total paid
- 6859.39
- Interest in the first month
- 95.42
- Payment exceeds the interest 1 means yes. If it is 0 the balance never falls.
- 1
Show the working
- Balance = 5000
- Annual percentage rate = 22.9
- Monthly payment = 200
- i = 22.9 / 100 / 12 = 0.019 083 3
- Interest in the first month = 5000 * 0.019 083 3 = 95.4167
- Payment exceeds the interest = 200 > 95.4167 ? 1 : 0 = 1
- Months to clear = 1 > 0 ? (0.019 083 3 == 0 ? 5000/200 : log(200 / (200 - 5000*0.019 083 3), 1 + 0.019 083 3)) : 0 = 34.2969
- Years = 34.2969 / 12 = 2.858 08
- Total paid = 200 * 34.2969 = 6859.39
- Total interest = 6859.39 - 5000 = 1859.39
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- months = log(payment / (payment - balance x i)) / log(1 + i), with i the monthly rate
- The logarithm only exists when the payment is bigger than the monthly interest.
If the payment is below the monthly interest the balance grows without limit and the calculator reports zero months, which is the honest answer.
This is arithmetic, not financial advice. Real products carry fees, tax treatment and terms that no formula captures.