Credit card payoff calculator

How the formula works

A credit card balance grows by the monthly rate \(i = \mathrm{APR}/12\) and shrinks by whatever you pay. For a fixed payment \(M\) against a balance \(B\), the number of months to zero has a closed form:

The term \(B\,i\) is the first month's interest. If your payment is below it, the fraction inside the logarithm goes negative and the formula has no answer — meaning the balance grows forever no matter how long you pay. The calculator warns you when a payment is in that zone.

The minimum payment has no closed form because it changes every month. Issuers most commonly charge that month's interest plus 1% of the balance, with a floor around $35 — so the minimum is engineered to shrink the balance by only about 1% a month. The calculator simulates that formula month by month, next to your fixed payment, so you can see what the convenience costs.

What each input means

Card balance — \(B\)

What you owe today. If you are still charging on the card, the model understates the payoff time — it assumes no new purchases.

Interest rate — APR

The purchase APR from your statement. Card issuers actually accrue interest daily (APR/365 on the average daily balance), but monthly compounding at APR/12 lands within a dollar or two a month of it, and it is the standard way payoff time is computed.

Monthly payment — \(M\)

What you commit to paying every month, held constant. The power move on a card is exactly this: keep paying the original amount as the balance falls, instead of letting the payment fall with the minimum.

A worked example

The worksheet's defaults: a $6,500 balance at 24% APR, paying $200 a month.

• Monthly rate: \(i = 0.24/12 = 0.02\); the first month's interest is $6,500 × 0.02 = $130 — so $200 covers it with $70 to spare, and the balance actually falls.
• The closed form: \(n = -\ln(1 - 6500\times0.02/200) / \ln(1.02) = 53.0\) — a hair over 53 full payments, so the last few dollars spill into a final month: 54 months (4.5 years), with $4,103 of interest along the way.
• The minimum route on the same balance starts at $195 a month and shrinks with the balance. It takes about 18.9 years and $11,442 of interest — more than 176% of the original debt, paid again as interest.

Assumptions and limits

• No new charges land on the card. Every purchase during payoff extends the timeline beyond what is shown.
• Interest compounds monthly at APR/12. Issuers accrue daily on the average daily balance; the difference over a payoff is small but real.
• The minimum-payment formula modeled is interest + 1% of the balance with a $35 floor. Issuers vary — some use flat 2% of balance — but the shape and the lesson are the same.
• The APR is held constant. A missed payment can trigger a penalty APR of 30% or more, which this model does not include. Arithmetic, not advice.

Questions people ask

Why does paying the minimum take decades?

Because the minimum is recalculated on the shrinking balance. It is typically that month's interest plus 1% of the balance — so the principal falls by roughly 1% a month, and each month you pay less, which stretches the tail out for years. It is not a hidden fee; it is the arithmetic of a payment designed to keep the account open as long as possible.

Is a balance transfer worth it?

Often, if you do the math on the fee. A 0% intro card charging a 3–5% transfer fee turns the interest question into one number: the fee versus the interest you would pay over the same months at your current APR. The trap is treating the 0% window as breathing room instead of a deadline — divide the transferred balance by the number of intro months and pay that amount, or the leftover balance meets a normal APR at the end.

Which card should I pay first if I have several?

Mathematically, the highest APR first (the avalanche): every dollar there retires the most expensive debt. Behaviorally, the smallest balance first (the snowball) produces quicker wins that keep people going. The interest difference between the two is usually smaller than the cost of quitting halfway, so the honest answer is: the one you will actually finish.

Does card interest really compound daily?

Yes — issuers apply a daily periodic rate (APR/365) to each day's balance, which is why carrying a balance for even part of a cycle costs money. This calculator uses monthly compounding at APR/12, the standard simplification; on a typical payoff it differs from the daily calculation by a rounding error, not a conclusion.

Will paying the card down help my credit score?

Usually, and quickly. The second-largest factor in a FICO score is utilization — balances as a share of limits — and it has no memory: when the reported balance falls, the score responds within a cycle or two. Keeping utilization under about 30%, and ideally under 10%, is the commonly cited range.