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Credit Card Balance & Level-Payment Payoff Estimate

Estimate the level payment or continuous payoff term for an existing card balance under a fixed monthly-rate model.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

A 12,000 balance with no interest or new charges and payments of 1,000 per month is repaid in twelve months, totaling 12,000.

n = −ln(1 − P × r/payment) / ln(1 + r); at r = 0, n = P/payment

Worked example

Enter these known values and leave the other values blank.

Existing card balance
12000 USD
Annual rate for the monthly estimate
0 %/yr
Level monthly payment
1000 USD
Continuous estimated payoff duration
0:11:30.1875 yrs / mos / days
Modeled payment total
12000 USD

Assumptions and limitations

  • The annual nominal interest rate is divided by twelve. Payments occur at the end of equal monthly periods, with a constant nonnegative rate and no extra payments or fees.
  • A whole number of monthly periods describes scheduled equal payments. A fractional term is a continuous mathematical estimate; it is not a calendar payoff date or an exact final partial-payment amount.
  • Calculations retain precision internally and format money for display. Lender rounding, daily accrual, irregular dates and contractual charges can change an actual schedule.
  • The supplied interest rate is an input; this calculator does not recover an unknown rate from other values. Duration selectors use fixed conversion factors, not calendar dates.
  • No new transactions, cash advances, promotional rate changes, late charges or changing minimum-payment rules are included. Card issuers may calculate interest from daily balances.
  • The payment must exceed interest accrued in one modeled month. Multiplying a fractional payoff term by a full payment is a continuous estimate, not the actual last statement amount.

Common questions

Why is a payment equal to monthly interest insufficient?

It leaves principal unchanged. A positive balance requires a payment above monthly interest to reach zero in finite time.

Will the displayed duration match a card statement?

Not necessarily. Statement cycles, daily balances, fees and a final partial payment can differ from this monthly approximation.

References

Bookify handles zero interest explicitly as principal divided by the term and updates the corresponding inverse equations. Bookify requires positive payoff time and a payment above monthly interest when a balance remains.

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