True cost of minimum payments
Credit-card statements show the balance and the minimum and stop there. The numbers that decide everything are the years-to-payoff and the total interest paid — and they live nowhere on the printed statement.
Inputs
From the back of your statement. Typical retail card: 18–29%.
A fixed amount you'd pay each month, instead of the minimum.
Minimum-payment formula
Most US issuers use 1% of balance + accrued interest with a $25 floor. Your exact card may differ — Chase, Citi, Capital One each tweak the formula. Override below if your statement spells it out differently.
Your card's first-month minimum at these settings: $259
Three payoff scenarios
Assumptions and formula →
Method: month-by-month simulation, not a closed-form formula. The minimum-payment scenario has a phase transition: while 1% × balance + interestis above the $25 floor, the balance decays geometrically (each month it’s multiplied by 0.99); once the balance drops below the cutoff (about $810 at 25% APR), the $25 floor takes over and the payoff becomes standard fixed-payment amortization. A closed-form combining both phases would be ugly and brittle, so the simulation runs the correct rule each step.
Termination conditions: (1) balance reaches zero — done. (2) the monthly payment is less than or equal to the interest charge — asymptotic, labeled honestly. (3) 720-month cap (60 years) — labeled as asymptotic for display purposes, since anything beyond a working life is operationally identical to never.
Issuer variations.Real card-issuer minimums vary. Chase typically uses 1% of balance + fees + interest with no fixed floor when auto-pay is on. Citi uses 1% + interest with a $25 floor. Capital One tiers the percentage at high balances. Override the percent and floor fields above with whatever your specific card’s cardholder agreement says — the simulation handles any combination.
What this doesn’t model:annual fees, late fees, promotional 0% periods, or balance-transfer offers. If you’re carrying a balance, a balance-transfer card with a 12–18 month 0% intro APR is often the highest-leverage move available — but the math on whether it’s worth it is its own calculator.
Read the long-form derivation: Calculator 4 — True cost of minimum payments →