How credit card interest works: APR, daily interest and grace periods

A credit card advertises one number, the APR, but the interest that lands on a statement is the product of several smaller rules: a daily rate, a method for averaging the balance across the billing cycle, a grace period that can be kept or lost, and a benchmark that may move the rate without notice. This guide walks through each rule with the arithmetic shown, explains the simplification that DebtWren’s calculators use, and shows what a 2,000 balance at 24% turns into when only the minimum is paid.

APR and the daily periodic rate

APR stands for annual percentage rate. On a credit card it is the yearly cost of borrowing expressed as a percentage of the balance, before any compounding is taken into account. A card does not charge a year of interest in one go; it charges a small slice at a time. Most issuers in the United States work in days, so the first step on a statement is to convert the APR into a daily periodic rate:

On its own the daily rate looks harmless: on a 2,000 balance it is 2,000 × 0.000657534 = 1.315068, about 1.32 a day. The cost only becomes visible when that daily slice is multiplied across the thirty-odd days in a cycle and the twelve cycles in a year.

The average daily balance method

Because the balance changes as purchases and payments post, issuers need a rule for which balance the daily rate applies to. The method used by most US cards is the average daily balance: add up the balance at the end of each day in the cycle, divide by the number of days, then multiply by the daily rate and by the number of days. Where the balance does not change, the arithmetic reduces to balance × daily rate × days.

Many agreements go a step further and add each day’s interest to the balance before calculating the next day’s, so interest compounds daily within the cycle. On the example above that adds about 0.38 to the 39.45 (2,000 × (1.00065753430 − 1) = 39.83), under one percent of the charge, but it is the reason the charge on a statement can be a touch higher than the simple multiplication suggests.

Grace periods and why a carried balance forfeits them

Interest on purchases does not always apply. A grace period is the window between the end of a billing cycle and the payment due date, usually at least 21 days in the US, during which the statement balance can be paid without any interest on those purchases. The Consumer Financial Protection Bureau explains that a card is not required to offer a grace period at all, but where one exists it generally applies only when the previous statement balance was paid in full by the due date.

That condition is the part that catches people out. Paying in full one month and only part of the balance the next does not simply mean paying interest on the part left over. In most agreements, once a balance is carried the grace period is lost for the following cycle as well, so new purchases start accruing interest from the day they post rather than from the due date. Restoring the grace period typically requires paying two consecutive statements in full. The practical effect is that a card carrying a balance has, for interest purposes, no interest-free days on anything.

The monthly approximation DebtWren uses

Daily balances are the right way to reproduce a specific statement, but they need a day-by-day record of every transaction, which a planning calculator does not have. DebtWren’s tools, including the credit card minimum payment calculator and the debt payoff calculator, instead charge interest once a month at the APR divided by 12:

So the two approaches are never far apart; the monthly figure is the daily figure for an average-length month, and the gap each cycle is a matter of cents, up or down depending on how many days the cycle contains and when payments landed. Over a repayment plan lasting a year or two the differences largely cancel, and the monthly approximation stays within a small margin of what a card would actually charge. What it does not model is the grace period, daily compounding or separate rates for different balance types, which is why DebtWren describes its outputs as estimates and publishes the rules on its methodology page.

Compounding over time: the minimum payment path

A single cycle’s interest is small. The cost of a card comes from the way each month’s interest joins the balance and is itself charged interest the following month. The clearest way to see this is to take a balance and pay only the minimum. The figures below come from DebtWren’s engine using its monthly rule, with a minimum of 2.5% of the statement balance and a floor of 25, a common structure on US cards.

Continuing at the minimum, the balance takes 207 months to clear, a little over seventeen years, with 4,663.81 in interest on the original 2,000 and 6,663.81 paid in total. The minimum shrinks as the balance shrinks, which is what stretches the plan out: once the statement balance drops below 1,000 the 2.5% rule gives less than 25, so the 25 floor takes over from month 131. The first 130 months, under the 2.5% rule, take the balance only from 2,000 to about 976; the fixed 25 then clears the rest over the final 77 months.

The table is not an argument for any particular payment; it shows what the arithmetic of a 24% rate does when most of each payment is absorbed by the interest added since the previous one. Our guide to credit card minimum payments looks at how issuers set the minimum and what changes when it is raised.

Variable rates and benchmarks

Most credit card APRs are variable: the agreement defines the rate as a benchmark plus a fixed margin, and the APR moves whenever the benchmark does. In the US the benchmark is almost always the prime rate, which banks set in step with the Federal Reserve’s target range and which the Federal Reserve publishes in its H.15 release. A card described as “prime + 17.99%” would carry a 25.49% APR when prime is 7.50% and would change the day prime changes, with no separate notice required because the formula was disclosed when the account opened. The CFPB notes that a fixed APR, by contrast, can only be changed with advance notice and in limited circumstances.

In the UK, card rates are not usually tied to a formula in the same way, but lenders’ pricing follows the Bank of England’s Bank Rate, and many agreements reserve the right to vary the rate for reasons including changes in that benchmark. Either way, a plan built on today’s APR is only as good as that APR, and the order of debts in a payoff plan can change when one rate moves and another does not.

Promotional 0% rates and deferred interest

A promotional rate is a lower APR, often 0%, applied to a specific balance (new purchases, a balance transfer, or both) for a defined period. In the US a promotional rate on a new account must generally last at least six months. During the offer the promotional balance accrues no interest; when it ends, whatever remains is charged at the standard rate from that point onwards. Balance transfers usually carry a fee, typically a percentage of the amount moved, which is a cost in its own right even at 0%.

Deferred interest is different, and the distinction matters. Common on store cards and retailer financing offers described as “no interest if paid in full within 12 months”, deferred interest accrues from the purchase date at the standard rate but is held back. If the full promotional balance is cleared before the deadline, the accrued interest is waived. If even a small amount remains, the entire accrued interest for the whole period is added to the account. On a 2,000 purchase at 24% that can be up to roughly 480 of back-dated interest appearing in one statement if little of the balance was paid down during the year, and around 260 if it was paid down steadily, triggered either way by a balance of a few units left over.

Cash-advance and penalty APRs

A card agreement normally lists several APRs, not one. The purchase APR is the headline rate. The cash-advance APR applies to cash withdrawals, and on many cards to cash-like transactions such as money orders or gambling, and is often several points higher than the purchase rate, has no grace period and comes with a transaction fee. The balance-transfer APR may match the purchase rate or differ. A penalty APR, where the agreement includes one, can be applied after a payment is 60 days or more late; it is typically the highest rate on the card and, under US rules, must be removed from the existing balance it was applied to once six consecutive minimum payments have been made on time, although it may continue to apply to new transactions. Each balance type is tracked separately on the statement with its own daily rate, which is why one card can show three or four interest charges in a single month.

Reading the rate on a statement

US statements carry a box, usually headed “Interest charge calculation”, that lists each balance type with its annual percentage rate, the balance subject to interest rate (the average daily balance for that type) and the interest charge. Multiplying the balance subject to interest by the APR, dividing by 365 and multiplying by the days in the cycle reproduces the charge to within a fraction of one percent, the gap being daily compounding; the number of days in the cycle appears next to the statement period. A letter “v” or the word “variable” beside a rate usually marks it as variable. The same page shows the minimum payment warning: how long the balance would take to clear and what it would cost at the minimum, alongside the payment needed to clear it in three years.

UK statements present the same information in a different layout: a summary box with the interest rates by balance type, the interest charged for the period, and a prescribed warning that paying only the minimum will take longer and cost more; some issuers add a figure for how long that would take, but a computed estimate is not required as it is in the US.

Notes for UK readers

UK card adverts quote a representative APR, a rate that at least 51% of successful applicants are expected to receive; an individual applicant’s rate can be higher. The UK representative APR also folds any compulsory fees into the figure under a standard formula, so it is not directly comparable with a US purchase APR. On rate changes, the Financial Conduct Authority’s Consumer Credit sourcebook, in section CONC 6.7, sets out rules on how lenders handle interest-rate increases on credit cards, including giving notice and allowing the customer to reject the increase and repay at the existing rate, and it restricts increases for customers at risk of financial difficulty. Those rules exist; what any one lender does within them is set out in its agreement.

Running your own numbers

To see how a card balance behaves at its minimum, enter the balance, APR and the minimum rule from the agreement into the credit card minimum payment calculator; it reports the first minimum, the months to clear and the total interest using the monthly rule explained above. To plan a fixed monthly amount across several debts, the debt payoff calculator runs the same arithmetic in avalanche or snowball order, and our guide to debt avalanche vs snowball compares the two. If the question is whether a single new loan would cost less than the cards, the debt consolidation calculator puts both paths side by side.

Every figure in this guide can be reproduced by hand with the formulas shown: APR ÷ 365 for the daily rate, average daily balance × daily rate × days for a statement, and balance × APR ÷ 12 rounded to the cent for DebtWren’s monthly approximation.

This guide explains how things work in general terms. It isn’t financial, tax or legal advice. Spotted something out of date? Email errors@debtwren.com and we’ll check it against the source.