How credit card interest actually works
Credit card interest is calculated daily on the average daily balance. The daily rate is APR / 365. Each day, interest is added to your balance, and the next day's interest is charged on the new, slightly higher balance — pure compounding. This is why a 22% APR actually costs about 24.36% effective annually.
When you pay only the minimum, most of your payment goes to interest instead of principal, so the balance barely moves.
Paying $50 or $100 above the minimum has an outsized effect because the entire extra amount reduces principal, which reduces tomorrow's interest, which frees up more of next month's payment for principal — a snowball in your favor.