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How Credit Cards Charge Interest
APR, balances, and the cost of carrying debt
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Credit cards let you borrow money for purchases, but any balance you do not pay back by the due date can be charged interest. The interest rate is usually shown as APR, which means annual percentage rate. Understanding how credit card interest works helps you compare cards, plan payments, and avoid debt that grows faster than expected. This matters because small daily charges can add up to a large cost over months or years.
Most credit cards calculate interest using a daily periodic rate and an average daily balance. The card company divides the APR by 365 to estimate the daily rate, then applies that rate to the balance for each day in the billing cycle. If you carry a balance, new interest can be added to what you owe, and future interest may be charged on that larger amount. Paying more than the minimum and paying early can reduce the average daily balance and lower the interest charged.
Key Facts
- APR means annual percentage rate, the yearly cost of borrowing shown as a percent.
- Daily periodic rate = APR / 365, using APR as a decimal.
- Interest for one day = daily balance x daily periodic rate.
- Monthly interest is often estimated by interest = average daily balance x daily periodic rate x number of days in billing cycle.
- At 24% APR, daily periodic rate = 0.24 / 365 = 0.0006575, or about 0.06575% per day.
- Paying only the minimum lowers the balance slowly, so interest can keep the debt growing or make it take much longer to pay off.
Vocabulary
- APR
- APR is the annual percentage rate, which shows the yearly interest rate charged for borrowing money on a credit card.
- Daily periodic rate
- The daily periodic rate is the APR divided by 365, used to calculate interest for each day.
- Average daily balance
- Average daily balance is the sum of the balances for each day in a billing cycle divided by the number of days in that cycle.
- Minimum payment
- The minimum payment is the smallest amount the card issuer requires you to pay by the due date to keep the account current.
- Grace period
- A grace period is the time between the statement date and due date when you can avoid interest by paying the full statement balance.
Common Mistakes to Avoid
- Using APR as a monthly rate is wrong because APR is a yearly rate. Convert it to a daily or monthly rate before calculating interest.
- Ignoring the average daily balance is wrong because credit card interest depends on how much you owed each day, not just the balance on the due date.
- Paying only the minimum without checking the interest cost is risky because most of the payment may go toward interest instead of reducing the amount borrowed.
- Assuming a late payment only adds a fee is wrong because late payments can also remove the grace period, increase the APR, and make future borrowing more expensive.
Practice Questions
- 1 A credit card has a 24% APR and a balance of $500 for all 30 days in a billing cycle. Use daily periodic rate = APR / 365 to estimate the interest charged for the month.
- 2 A student has balances of 450 for 10 days, and $600 for 10 days in a 30 day billing cycle. Find the average daily balance, then estimate the monthly interest at 18% APR.
- 3 Two students each owe 25 on the due date, while Student B pays $100 before the billing cycle ends. Explain which student will likely pay less interest next month and why.