APR vs. APY: The One-Letter Difference That Changes the Number

APR and APY look like the same rate with a typo. They aren't. One letter separates them, and that letter stands for a mechanic — compounding — that quietly changes the dollar amount you earn or owe. Knowing which you're quoted, and which favors you, is one of the highest-leverage pieces of financial literacy. Here's the math, worked.

The core difference

APR — annual percentage rate — is the simple annualized rate without accounting for compounding within the year. APY — annual percentage yield — folds compounding in, reflecting what you actually earn or pay once interest is calculated on prior interest. For the same nominal rate, APY is always equal to or greater than APR, and the gap widens the more frequently interest compounds.

Nominal rate	Compounding	APR	APY	Gap
5%	Annual	5.00%	5.00%	0.00%
5%	Monthly	5.00%	5.12%	0.12%
12%	Monthly	12.00%	12.68%	0.68%
12%	Daily	12.00%	~12.75%	~0.75%
20%	Daily	20.00%	~22.13%	~2.13%

The pattern is clear: at low rates and infrequent compounding, APR and APY are nearly identical. At high rates with daily compounding — exactly the conditions of a credit card balance — the gap becomes large and works against you.

Why deposits quote APY

Banks advertise savings and CD yields as APY, and that's the honest convention for the saver. APY tells you the real, all-in annual return after the bank compounds your interest. When comparing two savings accounts, compare APY against APY — never an APY against an APR — because only APY captures the compounding that determines what actually lands in your account. A 4.00% APY genuinely returns 4.00% over a year; the underlying nominal rate that produces it is slightly lower, but APY is the number that matters for comparison.

Why loans quote APR

Lenders and card issuers quote APR. For an installment loan, the APR is a reasonable representation of cost because it's also required to bundle in certain fees. But for revolving credit cards, the stated APR understates the real cost, because card interest typically compounds daily. A card advertising a 24% APR is, in compounding terms, charging an effective annual yield closer to 27% on a carried balance. The issuer quotes the lower APR; your statement reflects the higher compounded reality. This is precisely why a card balance grows faster than the headline rate suggests, and why carrying a balance is more expensive than the number on the agreement implies.

The promotional sleight of hand

The detail promoters omit is compounding frequency. A "12% rate" means very different things compounded annually versus daily — a 0.75-point difference at that level, larger at higher rates. When a promotion states only a rate without specifying APR or APY and without naming the compounding frequency, you can't actually price it. The fix is to ask directly: is this APR or APY, and how often does it compound? On a deposit, you want the APY confirmed; on a loan, you want to understand that the APR is a floor on the real compounded cost.

A simple rule of thumb

Use one heuristic. For money you're earning — deposits — compare APY, because it's the true yield and the bigger, more honest number. For money you're paying — loans and especially cards — remember the APR understates the real cost once daily compounding is applied. If you only remember one thing: APY includes compounding, APR doesn't, and the difference is dollars, not semantics.

The verdict

APR and APY are not interchangeable, and the entire financial-products industry relies on people treating them as if they are. Deposits are quoted in APY because it flatters the saver and happens to be honest. Loans and cards are quoted in APR because it flatters the lender and hides what daily compounding actually charges. Learn to spot which you're looking at, always compare deposit yields APY-to-APY, and treat any card's stated APR as the optimistic floor on what a carried balance will really cost. One letter, a measurable difference in your money.