APR vs APY: the difference that costs you money

One letter, opposite intent, and a few hundred dollars a year for the average household.

APR and APY look almost identical. They both mean "annual percentage something." Lenders quote one and banks quote the other, and they sound interchangeable on a billboard. They aren't. The shortest version: APR understates the true cost of a loan, and APY states the true return on savings. Knowing which is which — and what each one leaves out — is worth real money.

The definitions, with the trick visible

APR (annual percentage rate) is the nominal yearly rate without considering how often interest compounds. If a credit card has a 24% APR and compounds daily (most do), you actually pay more than 24% over a year because the daily interest is itself accruing interest.

APY (annual percentage yield) is the effective yearly rate after compounding is folded in. If a savings account advertises a 5% APY, that's what you'll actually earn over a year on a static balance, regardless of whether the bank compounds daily, monthly, or quarterly.

Why the asymmetry? Regulation. In the US, lenders are required to quote APR for consumer loans (Truth in Lending Act) and banks are required to quote APY for deposit accounts (Truth in Savings Act). Each convention happens to flatter the institution: the lender's rate looks smaller than reality, the bank's rate looks bigger than the nominal one.

The compounding math, made small

The relationship between a nominal rate and an effective rate compounded n times per year is: 

APY = (1 + nominal_rate / n)^n − 1

For a 24% nominal rate compounded daily (n = 365): 

APY = (1 + 0.24/365)^365 − 1 ≈ 27.11%

So a card "with 24% APR" actually costs you about 27.1% per year on a balance you carry. A $5,000 balance left untouched for a year accrues about $1,355 of interest, not $1,200.

On the other side: a savings account paying "4.85% APR compounded daily" is paying 4.97% APY. That's the number you should compare across banks.

Where APR understates things even further

Mortgage APR has a second twist. It's supposed to capture upfront loan costs — origination fees, points, certain closing costs — by amortizing them across the life of the loan and folding them into the rate. That's a useful idea, but APR assumes you keep the loan for its full term. Almost nobody does. The median US mortgage gets paid off (via sale or refi) in under 10 years, not 30.

So when comparing two mortgage quotes:

  • If you'll keep the loan long, APR is the better comparison.
  • If you might sell or refinance in 5 years, the upfront fees matter more than APR makes them look, and the lower-rate-higher-fee option may be worse.

When APR vs APY actually matters in your life

Credit cards

Almost always quoted in APR, almost always compounded daily. The true cost of carrying a balance is meaningfully higher than the sticker number. A 24.99% card is really a ~28.4% card.

Mortgages and auto loans

Quoted in APR. Compounding is monthly, so the gap between APR and APY is smaller — a 7% APR mortgage has about a 7.23% effective rate. The bigger issue is fees baked into APR, as discussed above.

High-yield savings, money market, CDs

Quoted in APY by regulation, so the number you see is the number you get on a static balance. The trap is that the rate can change any day on a savings account (it's not locked like a CD), so today's APY is not a forward guarantee.

Investment returns

Investment "rates of return" are usually compound annual growth rates (CAGR), which is essentially APY. A fund advertising "10% annual returns over the last decade" means your money compounded at 10% per year, not that it earned 10% simple interest each year.

The short version

  • APR = nominal, before compounding. APY = effective, after compounding.
  • For loans, APY is bigger than APR. The gap grows the more often the loan compounds.
  • For savings, the bank already quotes APY. Compare APYs to APYs.
  • Mortgage APR is APR plus upfront fees — useful, but it assumes you keep the loan forever.
  • Run real numbers in an APR/APY calculator rather than trusting the headline rate.