Formula registry
Every calculator on this site runs on the formulas below — each cited to a primary source so you can verify the math yourself. This page renders directly from the same verified data files the calculators use, so it cannot drift out of step with them.
When a reference value changes — an issuer convention, an average rate — we update the source data and record it in the changelog below. The engine's own conventions (monthly accrual, cent-exact rounding, the rollover invariant) are stated on the methodology page.
Monthly interest accrualconvention
interest per month = balance x (APR / 12)Consumer Financial Protection Bureau, Ask CFPB answer 51: card companies calculate interest daily from a daily periodic rate on the average daily balance; the monthly convention shown here is the standard calculator approximation of that process.
Known gap: issuers compound daily on the average daily balance, so a real statement can differ by a few dollars.
Issuer minimum-payment formula
minimum = max(floor, pct x balance + interest and fees)Consumer Financial Protection Bureau, The Consumer Credit Card Market (December 2025): most issuers set the minimum payment at 1 percent of the cycle-ending balance plus finance charges and fees; all reviewed issuers set fixed dollar floors, which ranged from $15 to $50, with $40 the most common.
Known gap: your issuer's exact formula is in your cardholder agreement and may differ.
Fixed-payment amortization
each month: interest = balance x APR/12; principal = payment - interest; closed form n = -ln(1 - rP/M) / ln(1+r)Consumer Financial Protection Bureau, Ask CFPB answer 1943: with a fixed payment, each month's interest is computed on the remaining balance and the rest of the payment reduces principal, so early payments are mostly interest and the split reverses over time — the standard amortization mechanics this engine implements.
Debt snowball ordering
pay minimums on everything; direct all extra at the SMALLEST balance; roll freed minimums into the next debtConsumer Financial Protection Bureau, How to reduce your debt: the snowball method focuses on the smallest debt first while making minimum payments on the rest, then moves to the next smallest once it is paid off.
Known gap: snowball usually costs somewhat more interest than avalanche; the comparison tool shows the exact difference for your debts.
Debt avalanche ordering
pay minimums on everything; direct all extra at the HIGHEST APR; roll freed minimums into the next debtConsumer Financial Protection Bureau, How to reduce your debt: the highest-interest-rate method focuses extra payments on the debts with the highest rate of interest, which minimizes total interest paid.
Balance-transfer fee and promo math
fee = max(feeMin, feePct x balance); transferred balance = balance + fee; compare stay vs transfer at the same monthly paymentConsumer Financial Protection Bureau, Ask CFPB answer 53: a balance transfer fee is charged to move an outstanding balance to a different card, and it may be charged even on a zero percent interest rate offer.
Known gap: the fee is usually capitalized into the transferred balance, which this tool models and states on-page.
Deferred-interest retroactive charge
interest accrues silently from day one; if any balance remains at window close, ALL accrued interest is charged at onceConsumer Financial Protection Bureau, Ask CFPB answer 40: on a deferred interest plan, if you do not pay off the entire promotional balance in time, interest going back to the date of purchase is added on top of the remaining balance.
Known gap: accrual is modelled monthly on the declining balance; issuers compute it daily on average daily balance.
Credit utilization
utilization = balance / limit x 100, per card and across all cardsConsumer Financial Protection Bureau, Ask CFPB answer 318: keeping credit use below about 30 percent of total limits is the commonly cited guidance, and paying balances in full each month earns the best scores; utilization is reported both per card and overall.
Known gap: the 30% figure is guidance widely cited by the CFPB, not a scoring-model constant; this site never simulates a score.
Changelog
2026-07-31
Full formula registry for the payoff wing: fixed-payment amortization (CFPB 1943), snowball and avalanche ordering (CFPB debt-reduction guidance), balance-transfer fee math (CFPB 53), the deferred-interest retroactive charge (CFPB 40), and credit utilization (CFPB 318).
2026-07-31
Initial data packs: monthly-interest and minimum-payment formulas (CFPB), issuer minimum-payment conventions (CFPB December 2025 market report), and reference card APRs (Federal Reserve G.19, May 2026).
Found an error or an outdated value? Tell us — we treat formula accuracy reports as our highest-priority issues.
Disclaimer: These formulas are provided for informational and educational purposes only and are not financial, tax, or legal advice. Issuer formulas and rates change; always verify against the cited primary source before relying on a result. See our Terms of Service.