APR vs APY: why the same rate shows up as two different numbers

What's the difference between APR and APY?

APR is the nominal rate: you take the rate charged each period and add it up across the year, and you stop there. APY is the effective rate: you let each period's interest start earning interest too, and you report what the year actually comes to. Same underlying rate — one leaves compounding out, the other puts it in.

Because APY counts the interest-on-interest that APR ignores, APY is never the smaller of the two. They land on the exact same number only when interest compounds once a year, because then there's no in-between interest to compound. Every faster schedule — quarterly, monthly, daily — lifts the APY a little further above the APR.

That's the whole relationship. The gap between an APR and its APY is compounding and nothing else, which means you can't read either number correctly without knowing how often the account compounds.

How do you turn an APR into an APY?

One formula does it: APY = (1 + APR/n)ⁿ − 1, where n is the number of times a year interest is added. Split the APR into n equal pieces, grow the balance by one piece each period, and see where a year leaves you.

Take that 24.99% card. Cards almost always compound daily, so n is 365. The daily piece is 24.99% ÷ 365 = 0.068% a day. Compound that for a year and you get (1 + 0.2499/365)³⁶⁵ − 1 = 28.38%. The 3.39 points between 24.99% and 28.38% never appear on the statement, but you pay them.

Drag the frequency toggle below down to Yearly and the APY drops to meet the APR exactly. Push it back up to Daily and they separate. That movement is the entire idea — the rate on the slider never changed, only how often it compounds.

The same math runs backward for savings. An advertised 4.50% APY compounded monthly is really a 4.41% nominal rate — the bank quoted you the compounded figure because it's the bigger one. Solve the formula for APR and you get n × ((1 + APY)^1/n − 1).

Why do banks quote APR on loans but APY on savings?

Because two different laws tell them to. The Truth in Savings Act requires deposit accounts to advertise APY, and the Truth in Lending Act requires loans and credit cards to advertise APR. Neither is a loophole — they're consumer-protection rules meant to make products comparable.

The side effect is that each product ends up advertising its better-looking number. On money you earn, APY is the larger figure, so savings looks generous. On money you owe, APR is the smaller figure, so borrowing looks cheaper. Line the two up and the pattern is hard to unsee.

None of this is illegal, and the disclosed number is genuinely required. But it means the figure in the ad is the flattering one on each side. Compare a loan and a savings account on their headline rates alone and you're comparing an APR against an APY — two things measured differently.

Does the compounding frequency really change the number?

Yes, though less than people fear on the savings side. Hold the nominal rate flat at 6% and change only how often it compounds, and the APY climbs — but it climbs toward a ceiling, not forever.

The jump from yearly to monthly is 0.17 points. The jump from monthly all the way to daily is about a hundredth of a point. Past a point, compounding more often stops mattering much — daily and "continuous" compounding are almost the same number. So a savings account bragging about daily compounding over a monthly one is selling you a rounding error.

The gap grows with the rate, though, which is why it matters far more on a credit card than on a savings account. At 6% the yearly-to-daily spread is 0.18 points. At 24.99% it's 3.39. High rates and frequent compounding are exactly where APR and APY drift furthest apart.

When does the gap actually cost you money?

On a balance you carry. The clean case is a credit card you don't pay off. Carry $6,000 on that 24.99% card for a year and the daily compounding charges you $1,702.72, not the $1,499.40 the 24.99% would suggest if you multiplied it straight. That's $203.32 you'd have missed by reading the sticker rate as the real cost.

The escape hatch is the grace period. Pay your statement balance in full each month and new purchases are charged no interest at all — the APR never gets a chance to compound, so the whole APR-versus-APY question is moot. It only comes alive once a balance rolls over and starts collecting interest day after day. If you're stuck in that cycle, see how long paying only the minimum really takes.

On the savings side the gap runs the other way and it's smaller, but it's still the honest number to compare. Say one account advertises a 4.50% APY and another advertises a 4.45% rate without calling it anything. They look all but tied, the first a hair ahead. But if that second 4.45% is a nominal rate, converting it to an APY lifts it to about 4.54% — ahead of the first, not behind. A nominal rate converts up to a bigger APY (they match only if it compounds once a year), so the account that quoted the smaller-sounding figure can be the better one. Always compare APY to APY, or nominal to nominal, never one against the other.

The trap underneath all of this is the one that runs through most money math: a percentage means nothing until you know exactly what it's measured against and how often. It's the same reason the Rule of 72 can tell you how fast a rate doubles your money in the first place.

Frequently asked questions

Last reviewed July 2026. APR-to-APY figures use daily compounding (365 periods) for cards and monthly for savings, the common conventions; your account's disclosure states its own frequency. Rates shown are examples for the math, not offers from any lender.