Credit card interest is quoted as an annual rate but calculated every day. That mechanical detail explains several outcomes that otherwise look like billing errors.
The rate is divided into a daily figure
The annual rate is converted into a daily periodic rate, which is applied to the balance outstanding on each day of the billing cycle.
The daily charges are summed to produce the interest shown on the statement. Two accounts with the same closing balance can owe different amounts depending on when spending occurred.
Because each day's interest is added to the balance the next day's calculation uses, the charge compounds within the month rather than only across months.
The grace period applies only to a fully paid balance
Purchases usually attract no interest between the transaction date and the payment due date, provided the previous statement was paid in full.
That condition is the whole mechanism. Paying anything less than the full amount removes the grace period, and new purchases begin accruing interest from the day they post.
Restoring it generally requires paying the balance in full and often keeping it there for a further cycle, which is why a single missed full payment has a long tail.
Average daily balance methods differ in detail
Most issuers calculate interest on the average daily balance across the cycle, which means payments made earlier in the month reduce the charge more than the same payment made later.
Some agreements include the previous cycle's balance in the calculation, which extends the period over which a cleared debt continues to generate interest.
The method is stated in the account terms rather than on the statement, and it materially changes what a partial payment achieves.
Different balances carry different rates
A single card commonly holds purchase balances, cash advance balances and promotional balances, each with its own rate and its own treatment of the grace period.
Cash advances typically begin accruing immediately with no grace period at all, and often at a higher rate than purchases.
Payments above the minimum are generally applied to the highest-rate balance first under many regulatory regimes, but the minimum itself may be allocated differently.
Why small carried balances persist
A balance that seems trivial still removes the grace period, so the following month's purchases accrue interest from day one and the total grows faster than expected.
Interest posted at the end of a cycle becomes part of the balance the next cycle's daily calculation runs on, which is compounding in its ordinary sense.
Clearing the balance entirely, rather than reducing it, is what resets the mechanism. The difference between nearly zero and zero is larger than the amounts involved suggest.