Your credit card statement shows an APR, but that number is not what you actually pay over a year. Because the interest is added to your balance and then earns interest itself, the real yearly rate is always higher than the headline figure. Here is the simple math to find it before you carry a balance.
APR and EAR are not the same thing
Most credit cards quote a nominal annual percentage rate (APR) that is compounded daily, or sometimes monthly. Despite the word “annual” in its name, the APR is not a direct measure of what you pay over one year on a balance that stays untouched. The figure that does that is the effective annual rate, or EAR. In practice, card issuers work out the finance charge in a way that is exactly equal to compound interest compounded daily, even though the interest only shows up on your account at the end of the billing cycle.
The formula to convert APR into EAR
The conversion is a single line:
EAR = (1 + APR / n)n – 1
Here, n is how many times a year the interest is compounded: 365 for daily, 12 for monthly. In plain words, you split the yearly rate into n small slices, let each slice grow on top of the last one, and see where you end up after a year.
A real example with two common rates
Take a card quoted at 12.99% APR. Compounded daily, the effective annual rate is 13.87%. Compounded monthly, it is 13.79%. The gap looks small at this level.
Now take a high rate of 29.99% APR. Compounded daily, the EAR is 34.96%, and compounded monthly it is 34.48%. On a balance of 10,000 left untouched for a full year, the headline rate suggests 2,999 of interest, while the daily compounding actually produces about 3,496. That is nearly 500 more than the number printed in large type.
The higher the APR, the wider the gap grows, which is why this matters most on exactly the cards where people tend to carry a balance.
What if your card quotes a monthly rate?
Some people see the rate per month rather than per year. As an illustration (not a rate from any specific bank), suppose a card charges 3.5% a month. Multiplying by 12 gives an APR of 42%. But the monthly compounding turns that into 1.03512 – 1, which is about 51.1% EAR. On 10,000, that is roughly 5,111 of interest in a year, not 4,200.
Common mistakes to avoid
- Comparing cards by APR alone. Always check how often the rate compounds, since daily and monthly compounding give slightly different yearly results.
- Ignoring the grace period. Many cards add no interest at all when you pay the full balance by the due date, so the APR only bites when you carry a balance. Most consumers use a card for convenience and pay it off in full each month.
- Forgetting the fees. Penalty fees, such as one for missing a minimum payment on time, sit on top of the interest.
- Assuming rates are fixed. Card issuers can usually raise the interest rate within legal limits after giving written notice.
The takeaway
Before you carry a balance, convert the APR with the formula above and use the EAR to compare. If you want to see how interest builds up over time, our guide on how to judge a savings interest rate walks through the same compounding idea from the saver’s side, and flat versus declining interest on loans shows another case where the quoted rate hides the real cost.
