Credit card payoff calculator and formula

Enter what you owe on the card, the rate the card charges, and the payment you intend to make every month. It returns the number of months to clear the balance, the total you hand over, the interest inside that total, and how the very first payment splits between interest and the debt itself.

The payment field is a payment you hold steady, and it is the one number on this page you fully control. A required minimum behaves differently: it is usually recalculated from the balance each month, so it falls as the balance falls.

The model is deliberately bare. One balance, one rate, one payment, and nothing else: no annual fee, no late fee, no promotional rate that expires, no cash advance charged at its own higher rate, and no fresh spending. Every one of those pushes the real term past the one shown here rather than pulling it in.

A card balance behaves like an unsecured loan with no agreed end date. Interest is charged on what you owe, your payment covers that interest first, and whatever is left reduces the balance. Repeat until the balance reaches zero. The number of repeats has a closed form:

$$n = -\frac{\ln\left(1 - \frac{iB}{M}\right)}{\ln(1 + i)}$$

Here $i$ is the monthly rate, $B$ is the balance today and $M$ is the fixed monthly payment. On a $6,000 balance at 22.9 percent, $i = 0.229/12 = 0.01908333$, so month one charges $114.50 of interest.

The last payment is nearly always a short one, because $n$ almost never lands on a whole number. This page rounds up to the next whole month and collects only what is left on that final payment, which is why the total handed over is not simply the payment times the months. On a balance small enough to clear in a single month, that short final payment is the first payment too: the calculator only ever collects what is owed.

Look at what sits inside the logarithm. The term $iB/M$ is month one's interest divided by the payment, and everything depends on which of those two is bigger.

• Payment above the interest: the fraction is under 1, the bracket is positive, and you get a real number of months.
• Payment equal to the interest: the fraction is exactly 1, the bracket is zero, and the answer runs off to infinity. Every payment covers the interest and nothing else, so the balance sits still forever.
• Payment below the interest: the bracket goes negative and there is no answer to give.

In that last case the calculator shows no payoff date. That is not a rounding problem or a missing input. It means the unpaid interest is added to what you owe, the balance is larger next month than it is this month, and no number of payments that size will ever clear it. On a $6,000 balance at 22.9 percent, that line sits at $114.50 a month.

The expensive place to be is just above the line rather than below it. A payment of $125 does clear the card, and takes 132 months to do it. Sitting a whisker above the line is barely better than sitting on it: the formula is close to vertical there, so a payment a fraction of a cent above month one's interest returns a term measured in centuries. This page treats any payment that beats that interest by less than half a cent as sitting on the line rather than above it, because the two amounts round to the same cent, and a payoff date that far out is precision the arithmetic does not have.

The relationship is not proportional, which is the whole point of running the numbers. Going from $125 to $160 a month is 28 percent more money, and it cuts the term by 49 percent and the interest by 55 percent. Every extra dollar goes straight to the balance, and a dollar of balance removed in month one stops charging interest in every month after it.

The rate matters as much as the payment. A card quotes a nominal rate as its APR rather than the yearly figure you actually pay once compounding is counted, and the APR against APY calculator shows the size of that gap. To see the card payment alongside everything else you owe, use the debt-to-income calculator. For borrowing that already has a fixed term, the loan payment calculator runs the same arithmetic the other way round.

One thing the totals here do not do is discount. The $16,378.84 in the first example is eleven years of payments added up in the money of the year each one is made, as though a dollar handed over in year eleven and a dollar handed over today were the same size. They are not, and the inflation calculator puts a figure on the difference.

A card statement in the United States usually carries a box comparing what the minimum payment costs with what a fixed payment that clears the balance in three years costs. That box is this calculation, run twice. Statements written to other countries' rules carry their own version of it, or none at all.