Where a minimum payment stops working

A minimum payment is recomputed every month from the balance that month, and how much of it reaches the balance depends on the rule the issuer uses and on the rate. This study sweeps both common rule shapes across a declared grid of balances and rates rather than sampling them, and locates each rule's boundary by measurement.

Where the balance does not fall at all, the engine reports that as its own outcome and distinguishes a balance that climbs from a balance that is exactly level. Both are counted here, separately, and so is the region where a payoff exists but runs past any horizon a reader is planning for.

What the data shows

• Under the flat-percentage rule the first payment's contribution to the balance falls to 0.83% at the extreme, and is under a tenth of the payment in 64 combinations. Under the interest-plus-a-percent rule it never fell below 26.09% anywhere in the grid.
• The flat-percentage rule has a sharp boundary. Above a balance of $1,250.00, where the percentage beats the dollar floor, it stops reducing the balance at exactly 24% APR — the same figure at every one of the 6 balances swept.
• Below that balance the dollar floor is the payment instead, so the boundary follows balance multiplied by rate rather than rate alone: balance multiplied by rate lands on the same figure — 30,000 — at each of the 2 balances swept below it.
• The practical cliff arrives well before the arithmetic one. The balance does fall in 110 combinations under the flat-percentage rule, but only past 40 yr — a term this study counts as a payoff no reader is planning for. Under the interest-plus-a-percent rule it happens in none of them.
• The grid accounts for itself: 1,608 combinations pay off, 263 never reduce the balance, and 1 the engine refuses outright as beyond anything it will model — a refusal, so that combination publishes no term and no interest at all.
• A balance that holds exactly flat is its own outcome, not a slow payoff and not a growing debt: 7 of the 263 non-reducing combinations sit exactly on that line.

• this month's interest plus 1% of the balance, with a $25 floor
• 2% of the balance, with a $25 floor

Drawn at a balance of $5,000.00 — one row of the 8 in the grid. Above the dollar floor this share does not depend on the balance, but the floor-bound rows below it reach lower than any line here: the thinnest figure in the table comes from one of them. The table and the download carry every balance.

• this month's interest plus 1% of the balance, with a $25 floor
• 2% of the balance, with a $25 floor

Drawn at a balance of $5,000.00 — one row of the 8 in the grid; the table and the download carry every balance. 17 points beyond 40 yr are counted here rather than drawn, so the axis is not stretched by the tail.

The dataset

Showing 12 of 1872 rows. The complete dataset — every row and every column — is in the CSV.

Download the full dataset (CSV) 1872 rows · 11 columns

The table shows the dataset's own rows, formatted as this site formats money and terms. The download carries the same rows unformatted, which is what a spreadsheet wants.

What was varied

Balances

$500.00 · $1,000.00 · $2,000.00 · $3,000.00 · $5,000.00 · $7,500.00 · $10,000.00 · $15,000.00

Rates

5% to 34% in steps of 0.25% — an exhaustive sweep, not a sample

Minimum payment rules

this month's interest plus 1% of the balance, with a $25 floor · 2% of the balance, with a $25 floor

Boundary sweep (separate from the grid)

A second pass, outside the grid above: 1% to 90% in steps of 0.01%, run at each balance to locate the rate at which each rule stops reducing the balance. Balances below the floor crossover have boundaries far above the grid's own ceiling, so those rows appear in this sweep and not in the download.

Seed

not seeded — an exhaustive sweep of a declared grid, not a sample

What was held constant

Minimum payment (this study's subject)

Minimum-payment behaviour IS this study's subject. Both rule shapes are varied across the whole grid and the minimum is recomputed every month from that month's balance — which is what a real minimum does, and what makes a minimum-only payoff so long.

Behaviour

Nothing is charged to the card again, no fee is added, the rate never changes, and the payment is always exactly the minimum due.

Rule shapes

Both are common United States card-issuer shapes rather than a universal formula. Neither is asserted to be the minimum payment rule, and a real agreement may differ.

Practical horizon

40 yr — this study's own threshold, not the engine's. The engine refuses only past a thousand years, so a balance falling by a rounding error each month would otherwise be reported as a payoff.

Plan anchor

January 2026 — pinned, so a rerun on any day produces identical output. These studies report terms and interest, never dates, so the anchor changes no published figure.

Data

Synthetic throughout. No customer data was used, approximated or fitted, and nothing here is a claim about what borrowers actually owe.

Engine version

payoff-25e86113b543

How this was computed

Every balance was run against every rate in the declared range, under each minimum-payment shape, using the engine's minimum-only schedule. That schedule recomputes the minimum every month from the balance that month, which is what a real minimum does and what makes a minimum-only payoff so long.

Where the balance does not fall at all, the engine reports that as its own outcome and distinguishes a balance that grows from a balance that holds exactly level. Both are counted here, separately.

What the model assumes

Nothing is charged to the card again, no fee is added, the rate never changes and the payment is always exactly the minimum due. The dollar floor and the percentage in each shape are named in the method block; a real agreement may differ, and yours is what governs.

Both shapes here are common United States card-issuer shapes rather than a universal formula. Neither is asserted to be the minimum payment rule.

What this does not show

It does not show how many cards carry either shape, or what any issuer actually charges. It shows what each declared shape implies.

The practical horizon used on this page is our threshold, not the engine's. The engine will model a payoff running for centuries; a term that long is arithmetically a payoff and practically not a payoff, so the count beyond the threshold is reported separately rather than folded into the rest.

Synthetic data, and why

Nothing here is drawn from customer accounts. This study is not even a sample: it is an exhaustive sweep of a declared grid, so there is no seed and no sampling error — only the assumptions, which are listed above.

Sources

1. Consumer Financial Protection Bureau — The box on your statement: paying off the balance in three years (tier 1)
2. Consumer Financial Protection Bureau — How does my credit card company calculate the amount of interest I owe? (tier 1)

Our source and corrections policy explains how these are chosen.

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