ABC Tools

Credit Card Payoff, Explained

After reading this you can work out how many months a fixed payment takes to clear a card, how much of that goes to interest, and what monthly payment hits a deadline you choose.

What this calculator answers

A credit card balance shrinks each month by the payment you make, and grows each month by the interest charged on whatever is still owed. Those two forces run at the same time. The question people actually want answered is simple: given a balance and an interest rate, when does a fixed payment reach zero, and what does the interest add up to along the way?

Consider a 5000 balance at 21% APR. Pay 200 a month and you are debt-free in 32 months, having paid about 1305 in interest. Pay 300 instead and you finish in 19 months with roughly 708 in interest. The extra 100 a month cuts 13 months and 597 in interest. That leverage, larger than most people expect, is the point of running the numbers.

The tool works in two directions. In payment mode you give a monthly payment and it finds the number of months. In months mode you give a deadline and it finds the payment required to meet it.

When to use it, and when not

Use it when you carry a balance on one card, pay a fixed amount each month, and the APR is a single steady rate. That describes most everyday card debt.

It fits less well in a few cases. If you have several cards, the order you attack them matters, so compare strategies with the Debt Snowball vs Avalanche tool. If you are tempted to pay only the minimum, the minimum itself falls as the balance drops, which this fixed-payment model does not capture; the Minimum Payment Trap Calculator handles that shrinking payment. And if the debt is an installment loan rather than revolving card debt, the Loan Calculator is the closer match.

The model assumes you stop adding new charges to the card. Every new purchase resets the arithmetic. If you keep spending on the card while paying it down, the payoff date shown here is optimistic.

The formula and the intuition behind it

Start with the monthly rate. An APR is an annual figure, so divide by 12:

i = \frac{\text{APR}}{1200}

Here i is the monthly interest rate as a decimal. At 21% APR, i = 21 / 1200 = 0.0175, so 1.75% is added to the balance each month.

Each month the balance updates by one multiply and one subtract. If B_n is the balance after month n and P is the payment:

B_{n} = B_{n-1}(1 + i) - P

Interest is applied first, then your payment comes off. Iterating this until the balance reaches zero gives an exact month count, and it is how the tool computes results. It also has a closed form. Solving the recurrence for the number of months N gives:

N = \frac{-\ln\left(1 - \frac{i B}{P}\right)}{\ln(1 + i)}

Here B is the starting balance, P the monthly payment, i the monthly rate, and \ln the natural logarithm. The result is usually not a whole number; the final month is a partial payment, so round up to count whole months.

The term 1 - \frac{iB}{P} must be positive, which means P \gt iB. If your payment is smaller than the monthly interest charge, the balance grows every month and never reaches zero. At 21% APR on 5000, the interest alone is 0.0175 * 5000 = 87.50 a month, so any payment at or below 87.50 never clears the debt.

Turning the deadline around

In months mode you fix N and solve for the payment. Rearranging the same recurrence gives:

P = \frac{B \cdot i (1 + i)^N}{(1 + i)^N - 1}

This is the standard amortized-payment formula, the same one behind any fixed-term loan. Feed it a balance, a monthly rate and a month count, and it returns the level payment that lands the balance exactly on zero at month N.

Reproducing the demo: 5000 at 21% paying 200

These are the tool's default values, so you can click Calculate and check each step.

  1. Monthly rate: i = 21 / 1200 = 0.0175.
  2. Check feasibility: interest in month one is 0.0175 * 5000 = 87.50, well below the 200 payment, so the balance falls.
  3. Compute the inner term: \frac{iB}{P} = \frac{0.0175 \times 5000}{200} = 0.4375, so 1 - 0.4375 = 0.5625.
  4. Take logs: -\ln(0.5625) = 0.5754 and \ln(1.0175) = 0.017349.
  5. Divide: N = 0.5754 / 0.017349 = 33.17 months, so 34 whole months to fully clear it.

Total paid is roughly 33 * 200 + partial ≈ 6634, so interest is about 1634. Small differences from a rounded hand calculation come from the last, partial payment. The month-by-month engine in the tool tracks that final month exactly.

Reading the results

Two numbers carry most of the meaning: the month count and the total interest. The interest is what the debt costs you on top of the amount you borrowed. On a 5000 balance, paying 1634 in interest means you handed over about a third again on top of the original balance.

The most useful thing to watch is how sensitive both numbers are to the payment. The relationship is steeply curved, not straight. Doubling your payment more than halves your interest, because a larger payment attacks the principal earlier, and less principal means less interest compounding in every later month.

The curve drops fast at first, then flattens. Near the left edge, small payments barely beat the interest, so months explode toward infinity.

At 21% APR on a 5000 balance: paying 150 a month takes about 64 months (1596 interest), 200 takes 34 months (1634 interest is lower per month but months help), 300 takes 19 months (708 interest), and 500 takes 12 months (415 interest). Larger payments cut both months and total interest sharply.

Common mistakes

Confusing APR with the monthly rate
21% is annual. The monthly figure that actually hits your balance is 1.75%. Plugging 21 into a monthly formula overstates the cost by roughly twelve times.
Assuming interest is fixed
Interest is charged on the remaining balance, so it falls every month as you pay down. In the demo the first month's interest is 87.50 but a later month's is a fraction of that. This is why total interest is far less than 34 times the first month's charge.
Paying at or near the interest-only line
A payment just above 87.50, say 100, technically clears the 5000 debt but takes about 83 years and costs more than 5000 in interest. The last few dollars of payment do almost nothing; the first few above the threshold do almost nothing either.
Forgetting new spending
The math assumes the balance only goes down. Charging 100 of groceries to the card each month while paying it off cancels much of your progress.
Trusting the monthly model as exact
Card interest usually accrues daily and compounds, so real costs run slightly higher than this monthly model shows. Treat the results as a close estimate, not a statement from your issuer.

Related tools

Once you know your payoff figures, a few neighbouring calculators help you decide what to do next. To see whether one lower-rate loan beats several card balances, use the Debt Consolidation Calculator. To check how much a lump-sum or recurring extra payment saves on an installment loan, try the Extra Loan Payment Calculator. To judge whether a new loan's fees are worth the lower rate, the APR from Fees Calculator and the Loan Comparison Calculator both help. If you want to know how your total debt stacks against your income, the Debt-to-Income Ratio Calculator gives the 28/36 verdict lenders use.

Frequently asked questions

Why does my card statement show a different payoff time?

Issuers compound interest daily and may use the average daily balance, while this tool applies one monthly interest step. The daily method costs a little more, so your statement's figure is usually slightly higher. The gap is small for typical balances but grows with the rate.

What payment clears my card the fastest without wasting money?

Every extra dollar above the interest-only threshold shortens the payoff, so there is no single sweet spot. The savings per extra dollar shrink as the payment rises. The practical answer is the largest amount you can sustain every month without missing it elsewhere.

Does making two payments a month help?

A little, because paying earlier in the cycle means slightly less interest accrues before the balance drops. This monthly model cannot show that effect; it treats payments as one lump per month. The saving is real but usually modest.

What if my payment is below the monthly interest?

The balance grows every month and the debt never clears. At 21% APR on 5000 the interest is 87.50 a month, so any payment at or under that amount leaves you worse off over time.

Is the total interest figure before or after tax?

It is the raw interest charged by the card, before any tax treatment. Personal credit card interest is generally not tax deductible, so the figure is what leaves your pocket.

Try it yourself in the tool

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