APR vs APY: How to Convert Between Them and Stop Comparing the Wrong Numbers

I once spent twenty minutes comparing two savings accounts before realizing the bank had quoted one in APR and the other in APY. They are not the same number, and the difference is exactly where a worse rate gets dressed up as the better deal. If you have ever stared at a 4.9% and a 4.95% and felt unsure which actually pays more, this guide is for you — and the APR to APY Calculator does the conversion for you in two clicks.

What APR and APY actually mean

APR stands for Annual Percentage Rate. It is a nominal rate: it states the yearly rate without folding in any compounding that happens during the year. APY stands for Annual Percentage Yield, sometimes called the effective annual rate or EAR. It folds compounding in, so it tells you what you genuinely earn or pay over a full twelve months.

Here is the part that trips people up. A 12% APR compounded monthly is not a 12% return. Each month earns 1%, and that 1% itself earns interest in the following months. By December the effective figure is 12.6825% APY. The only time APR and APY are equal is when interest compounds exactly once per year — annual compounding leaves nothing to roll up mid-year.

The math behind the conversion is a single closed-form expression:

APY = (1 + APR / n)^n − 1

where n is the number of compounding periods per year. For continuous compounding the formula becomes e^APR − 1, and the inverse direction (solving for the APR that hits a target APY) is APR = n × ((1 + APY)^(1/n) − 1).

How compounding frequency moves the number

Frequency matters, but not uniformly. The jump from annual to monthly is large; the jump from daily to continuous is almost nothing. Take a single 10% APR and run it through every frequency:

• Annual: 10% APY
• Semi-annual: 10.25% APY
• Quarterly: 10.47% APY
• Monthly: 10.4713% APY
• Daily: 10.5156% APY
• Continuous: 10.5171% APY

That last gap — daily to continuous — is about 0.0015 of a percentage point. This is diminishing returns made concrete. Continuous compounding is the mathematical ceiling, the limit as compounding periods approach infinity, and in the real world almost nothing reaches it. It is the standard convention in options pricing and bond math, but for a normal bank account, daily compounding is already within a hair of it.

The size of the APR-to-APY gap grows with both the rate and the frequency. At 5% APR, monthly compounding gives a 5.12% APY — a 0.12 point gap. At 24.99% APR compounded daily, the APY is about 28.39% — a 3.4 point gap. The bigger the rate, the more the hidden compounding adds up.

Why deposits quote APY and loans quote APR

Each side of a financial product quotes whichever number looks better for what it is selling.

For a deposit, APY is the larger figure once daily or monthly compounding is added, so it makes the return look more attractive. This is not just marketing preference: in the United States, the Truth in Savings Act and its implementing rule, Regulation DD (12 CFR Part 1030), require depository institutions to disclose the Annual Percentage Yield so consumers can compare savings products on a consistent, apples-to-apples basis. Regulation DD even specifies the APY calculation formula in its appendix.

For a loan or credit card, the lender quotes APR — the smaller, less alarming number — even though daily compounding means your true cost is the higher APY. The Truth in Lending Act governs that side and requires APR disclosure. The result is two products described in two different units, which is precisely the trap I fell into.

The fix is to convert everything to a single unit before you compare. Convert the loan's APR to its real APY, or convert the deposit's APY back to a nominal APR — either works, as long as both products end up in the same column.

A worked example: the credit-card APR you actually pay

Let me walk through a real case. Your card statement says 24.99% APR. Issuers compound daily, so the rate you truly pay when you carry a balance is the APY, not the APR. Enter 24.99 into the calculator, pick daily compounding, and you read 28.39% APY — a 3.4 point premium the APR alone hides.

On a $5,000 balance, that gap is roughly $170 a year you would never have predicted from the stated rate. The input is one number and one dropdown; the output is the effective rate plus the spread between the two figures, so you can see exactly how much intra-year compounding costs you.

The reverse direction is just as useful. Say you are structuring a promo and want a product to deliver a clean 5% APY on a monthly-compounding account. Switch the tool to APY → APR, type 5, pick monthly, and it returns about 4.889% APR. Now you know the nominal rate your term sheet needs to quote to land on that yield.

Three mistakes to avoid

1. Comparing an APR against an APY directly. A 4.9% APR and a 4.95% APY are not what they look like side by side. Convert both to the same unit first.
2. Forgetting to set the compounding frequency. The same APR produces a different APY at daily, monthly, and annual compounding. Pick the frequency the disclosure actually uses, or the number means nothing.
3. Assuming continuous compounding for a normal product. It is a theoretical ceiling. Use daily or monthly for real accounts; reserve continuous for coursework and derivatives math.

Once you have the rates lined up in the same unit, the rest of your planning gets easier. If you want to see how an effective rate grows your balance over years, pair the conversion with the Compound Interest Calculator to project the actual dollar outcome — the APY you just computed is exactly the rate that calculator wants as its input.

APR and APY are two different views of the same loan or deposit. Knowing which one you were handed, and converting it to the other, is the difference between a confident comparison and a guess.

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Made by Toolora · Updated 2026-06-13