Card Payoff Schedule Calculator and Formula

A card payoff schedule estimates how many monthly payments it will take to clear a credit-card balance and how much interest those payments add. Enter the balance, APR, and planned monthly payment to see the estimated payoff time and total paid; the calculation assumes a constant rate and payment.

Formula

The schedule treats the card balance as a loan that accrues interest monthly, with a fixed payment made at the end of each month. It estimates months to payoff using the level-payment repayment formula:

n = ceil(round(-ln(1 - r × B / M) / ln(1 + r), 6))

• B is the starting balance in dollars.
• APR is the annual percentage rate entered as a percentage, such as 18 for 18%.
• r is the monthly rate, calculated as APR ÷ 1200.
• M is the planned monthly payment in dollars.
• n is the estimated number of monthly payments, rounded up to a whole month.

Total paid is estimated as M × n, and estimated interest is total paid minus the original balance. This simplified total assumes the same payment is made every month, including the final month. In practice, the last payment is often smaller, so actual totals may be lower than this estimate.

Worked Example

Using the default inputs: balance $5,000, APR 18%, and monthly payment $250.

1. Convert APR to a monthly rate: r = 18 ÷ 1200 = 0.015, or 1.5% per month.
2. Substitute into the payoff formula: n = ceil(-ln(1 - 0.015 × 5000 ÷ 250) ÷ ln(1.015)).
3. Calculate the inside value: 1 - 75 ÷ 250 = 0.7. Then -ln(0.7) ÷ ln(1.015) ≈ 23.99, which rounds up to 24 months.
4. Estimated total paid: $250 × 24 = $6,000.
5. Estimated interest: $6,000 - $5,000 = $1,000.

The calculator therefore estimates 24 months to payoff, $6,000 paid, and $1,000 in interest under its fixed-payment assumptions.

Assumptions

• The APR and monthly payment remain fixed for the entire payoff period.
• Payments occur once per month, after that month’s interest accrues.
• Interest compounds monthly at APR ÷ 12.
• The estimate excludes new purchases, cash advances, balance transfers, fees, penalties, and any changes in payment or rate.

How to Read a Card Payoff Schedule

The month count is an estimate of the number of regular payment periods needed to reduce the balance to zero. The total paid and interest figures make the cost of carrying the balance easier to understand, but they are not a statement from a card issuer. A real statement may show a different result because card interest can depend on daily balances, transaction dates, payment dates, and the account’s terms.

The key threshold is the interest charged during a month. At an 18% APR, the simplified monthly rate is 1.5%; on a $5,000 balance, one month’s interest is approximately $75. A payment of $75 or less would not reduce the balance under this model. The calculator reports that it cannot compute a payoff schedule when a payment does not exceed the first month’s estimated interest.

This threshold can change as the balance changes, but a fixed payment above the initial interest amount continues to reduce the balance in the model. If the payment is only slightly above that amount, payoff can take a very long time.

Using the Estimate Carefully

Enter the card’s current balance, not its credit limit, and use the APR that applies to the balance being considered. A card can have different rates for purchases, cash advances, or transferred balances. If amounts are subject to different rates, calculating each separately may provide a clearer estimate than treating the entire account as one balance.

• Payment changes: If you expect to make a different payment each month, this fixed-payment formula will not reproduce that pattern.
• New charges: Purchases added while paying down a balance can extend payoff and increase interest.
• Rate changes: A variable APR or promotional rate ending during the schedule can change the result.
• Rounding: The formula rounds the calculated month count up to a whole month and assumes a full planned payment in every month. Actual final payments are commonly adjusted to the remaining balance and interest.

For a practical month-by-month schedule, calculate interest on the current balance, subtract the resulting payment after accounting for interest, and repeat. The actual issuer’s calculation method and statement remain the source for the amount due and payoff figures.

Common Misconceptions and Limits

A minimum payment is not necessarily a fixed payment: issuers can determine it using account-specific terms, and it may change as the balance falls. This calculator does not determine a card’s minimum payment. Enter an intended monthly amount instead, and check the card statement for the amount currently due.

Also, APR is not always the exact rate used for each day of a billing cycle. The calculator converts APR to a monthly rate for a compact estimate; card issuers may calculate interest using daily periodic rates and average daily balances. Fees, grace-period treatment, new transactions, and payment timing can also affect the actual amount. The formula is useful for comparing hypothetical payment amounts under the same assumptions, not for predicting an exact statement balance.

Frequently Asked Questions

How do I calculate how long it will take to pay off a credit card?
Use the starting balance, APR, and planned fixed monthly payment in the payoff formula. The result estimates whole months, provided the payment exceeds the first month’s estimated interest.

Why does the calculator say it cannot compute?
The payment may be no greater than the estimated monthly interest on the starting balance. In that case, the formula cannot produce a payoff under fixed-payment assumptions.

Does this include new purchases or fees?
No. It assumes no new charges or fees and a constant APR. Additions to the balance or account charges can change the time and cost.

Is the final payment really the same as the monthly payment?
Not necessarily. The calculator multiplies the planned payment by the estimated number of months for a simple estimate; an actual final payment is often adjusted to the amount remaining.

Why does my card statement show different interest?
A statement may use daily balance calculations, different transaction rates, payment timing, fees, or changing APRs. This monthly model simplifies those details.

This result is an estimate for educational use, and the card issuer’s disclosure gives the exact figures.

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in bal | Card balance | $ | 5000 | 0.01 | 100000000
in apr | Interest rate (APR) | % | 18 | 0.01 | 100
in pay | Monthly payment | $ | 250 | 0.01 | 100000000
out mon | Months to payoff | months | ceil(round(-ln(1 - (apr / 1200) * bal / pay) / ln(1 + apr / 1200), 6)) + 0 * sqrt(pay - (apr / 1200) * bal) | 0
out tot | Total paid | $ | pay * mon | 2
out int | Total interest | $ | pay * mon - bal | 2