What minimum payments really cost you
Your minimum shrinks as your balance drops. Following it down is what stretches a balance across decades.
Why the minimum shrinks
Your minimum is a formula, not a fixed bill. Most issuers set it at one month of interest plus about 1% of the principal. As the balance drops, both parts drop. Pay a little, owe a little less, get asked for a little less next month.
Nothing hidden is happening. The structure simply favors the card company, and following it costs you decades.
Read the full explanation in What minimum payments really cost you.