The statutory disclosure is the spine of this subject, and it can be quoted exactly. 12 CFR 1026.7(b)(12)(i)(A) requires every credit card periodic statement, with limited exceptions, to carry the following words under a bold heading: "Minimum Payment Warning: If you make only the minimum payment each period, you will pay more in interest and it will take you longer to pay off your balance." That is Congress legislating a sentence onto a bill, which is rare, and it tells you how the practice was viewed.
The rest of the box does more. Subparagraph (B) requires the minimum payment repayment estimate, in months where it is under two years and otherwise in whole years. Subparagraph (C) requires the total cost estimate at minimum payments. Subparagraph (F) then requires, in most cases, a second column entirely: the estimated monthly payment that would clear the balance in 36 months, a statement that paying it each month for three years would repay the balance shown, the total cost of doing so, and the savings against paying minimums. So the regulation does not merely warn. It puts a side-by-side comparison of two repayment paths on the statement, with the difference in dollars.
Three qualifications keep that description honest. The 36-month block is not always shown. Under (b)(12)(i)(F)(2) it is switched off where the minimum-payment payoff estimate already rounds to three years or less, where the calculated 36-month payment would be smaller than the minimum required that cycle, and in a defined case involving an account with both a revolving feature and a fixed repayment feature. The whole disclosure is exempt for charge card accounts requiring payment in full, for a cycle following two consecutive cycles paid in full or at zero, and for a cycle where the minimum payment would clear the balance anyway.
The estimates are counterfactual by construction, and that is the point most readers miss. Subparagraph (D) requires a statement that the figures are based on the balance shown and on the assumption that only minimum payments are made and no other amounts are added to the balance. A cardholder who keeps using the card is not in that scenario, so the real payoff is longer and the real cost is higher than the box says. The box is not optimistic about minimum payments; it is optimistic about the reader's future spending.
There is a starker version of the disclosure for the worst case. Where the calculation produces negative or no amortization, 1026.7(b)(12)(ii)(A) replaces the standard warning with: "Minimum Payment Warning: Even if you make no more charges using this card, if you make only the minimum payment each month we estimate you will never pay off the balance shown on this statement because your payment will be less than the interest charged each month." A regulation that has to provide wording for that outcome is telling you it happens.
The compounding trap sits outside the disclosure entirely. Under 15 USC 1666b(b) the interest-free grace period applies only where the balance is paid in full, so a cardholder who pays the minimum has lost it. Next month's purchases begin accruing interest on the day they are made rather than after the due date. People model the cost of revolving as the rate on the balance they chose to carry, and miss that everything bought afterwards is now accruing from day one until the balance is cleared in full again. Cash advances typically have no grace period in the first place.
A note on framing, because the common version of it is not defensible. It is often said that the minimum is engineered to keep people in debt. What can be established is narrower and more useful: the minimum is set by each issuer to keep the account current while amortizing the balance slowly, no federal rule sets its size, and Congress's response to the resulting cost was to mandate disclosure rather than to impose a floor. Asserting what a private company intends is a claim nobody outside it can verify. The arithmetic below needs no such claim.