Last updated: 2026-05-06

What a credit card payoff calculator computes

A credit card payoff calculator determines how long it takes to clear a revolving balance and how much interest accrues over that period, given the balance, annual rate, and monthly payment. The same model runs in reverse to find the payment required to clear the balance by a chosen deadline, and it can simulate the case where only the card issuer's minimum is paid each month.

A credit card balance is revolving debt: interest is charged on the outstanding balance each month, and any payment is applied first to that interest and then to principal. The payoff timeline therefore depends on the gap between the monthly payment and the monthly interest charge — the larger that gap, the faster the principal falls.

The amortization model

For a balance $B at an annual rate $r, the monthly interest charge is $B × r/12. A fixed monthly payment $P first covers that interest; the remainder reduces the principal. Because the principal shrinks each month, the next month's interest charge is smaller, so a constant payment retires the balance progressively faster.

Solving this recurrence in closed form gives the number of months to payoff:

$n = -\frac{\log\left(1 - \frac{B \cdot r/12}{P}\right)}{\log\left(1 + \frac{r}{12}\right)}$

Total repayment is $P × n, and total interest is $P × n − B. The payment must exceed the first month's interest charge ($B × r/12); otherwise the balance grows without bound and the formula has no solution. The calculator flags that case.

Worked example

On a $5,000 balance at 18% APR with a $200 monthly payment, the first month's interest is 5,000 × 0.18/12 ≈ $75, so $125 reduces the principal. Carried through the closed-form equation, the balance clears in roughly 32 months with about $1,400 in total interest.

Three modes

The mode selector switches between three forms of the same model:

• Time mode (default): the monthly payment is given, and the calculator returns the number of months to payoff.
• Payment mode: a target payoff term is given, and the calculator inverts the amortization formula to return the required monthly payment.
• Minimum-payment mode: the calculator simulates paying only the card issuer's minimum each month, defined by a percent-of-balance figure and a fixed floor.

The closed-form inverse used in payment mode solves the same equation for $P:

$P = \frac{B \cdot r/12}{1 - (1 + r/12)^{-n^*}}$

For a $5,000 balance at 18%, the required payment falls as the target term lengthens:

Payment mode fits a fixed deadline; time mode fits a fixed monthly budget.

The minimum-payment case

Many issuers calculate the monthly minimum as the higher of a percent-of-balance amount plus interest, or a fixed dollar floor, with the percent typically 1–3%. Because the percent component is applied to a shrinking balance, the minimum payment falls every month, which slows principal reduction.

While the percent term dominates, the balance decays geometrically:

$B(m) = B \cdot (1 - p)^m$

At a 1% percent term, the balance drops by about 1% per month. After 60 months it is still $B × 0.99⁶⁰ ≈ 0.55 B — a little over half cleared after five years. Once the percent-of-balance figure falls below the dollar floor, the schedule switches to standard amortization at the fixed floor, which is also slow.

On a $5,000 balance at 22% APR with a "1% of balance + interest, $25 floor" formula, month 1 breaks down as:

• Month 1 minimum: 5,000 × (0.01 + 0.22/12) ≈ $142
• Of that, interest: 5,000 × 0.22/12 ≈ $92
• Goes to principal: $50

The closed-form result is roughly 19 years to payoff and more than $8,000 in total interest — over 1.6× the original balance. Paying a fixed amount above the issuer's minimum removes the falling-payment effect entirely.

Effect of a larger payment

The leverage of a higher payment is large, because each additional dollar reduces both the principal and all the future interest that principal would have generated. On the same $5,000 at 22%:

Doubling the payment from $150 to $300 cuts total interest by about 65%.

The extra-payment slider

In time mode, any amount paid above the scheduled payment goes entirely to principal and saves the interest that principal would otherwise have accrued. The chart updates as the extra amount changes, and the gap between the actual balance curve and the baseline (no-extra) curve shows the savings. On a $5,000 balance at 18% with a $200 baseline payment:

• No extra: ~32 months, ~$1,400 interest
• +$50/mo: ~24 months, ~$990 interest — about 8 months and $325 saved
• +$100/mo: ~19 months, ~$800 interest — about 12 months and $517 saved
• +$200/mo: ~14 months, ~$580 interest — about 18 months and $735 saved

Each extra dollar of principal earns the card's APR as a return for as long as the balance would have lasted. At an 18–25% APR, that return is higher than most low-risk alternatives.

The balance curve

The chart sweeps the closed form across every month $m between 0 and $n:

$B(m) = B \cdot \left(1 + \frac{r}{12}\right)^m - P\_{\text{eff}} \cdot \frac{\left(1 + \frac{r}{12}\right)^m - 1}{r/12}$

where $P_{\text{eff}} = P + \text{extra}. The month slider reads off the remaining balance, cumulative principal paid, and cumulative interest paid at any point in the term.

Applications

Evaluating a balance transfer

A balance transfer moves debt to a new card with a 0% promotional APR, typically lasting 12–21 months, in exchange for an upfront fee of 3–5%. It reduces total cost when the balance is cleared before the promotional period ends. If a $5,000 balance at 22% would otherwise cost $1,750 in interest, a transfer to 0% with a 4% fee costs $200 — a difference of $1,550, conditional on full repayment within the promotional window. If the balance is not cleared in time, the post-promotional rate may exceed the original card's rate.

Ordering multiple balances

With several cards, two common orderings apply:

• Avalanche: pay the highest-APR balance first, which minimizes total interest.
• Snowball: pay the smallest balance first, which clears individual accounts sooner.

The avalanche method is optimal for total interest; the snowball method clears accounts faster, which some research links to higher follow-through (Gal & McShane, 2012). Running both orderings shows how large the interest difference is for a given set of balances.

What this model does not cover

• Late fees and penalty rates: a missed payment can trigger a penalty APR of 30% or more. The model assumes consistent, on-time payments.
• Rewards: cash back or points recover a small percentage of spending but do not offset the cost of carrying a balance.
• Variable rates: most card APRs track the prime rate and adjust periodically. The model assumes a fixed rate, which understates cost when rates rise.
• Credit-utilization effects: a balance above roughly 30% of the credit limit can lower a credit score, which affects future borrowing rates.
• Opportunity cost: the "interest saved" figure compares the same plan with and without the extra payment; it does not model returns from investing that money instead.

After the balance is cleared, the freed-up monthly payment can be redirected toward a savings target. The Savings Goal Calculator maps that cash flow against a specific goal.