Why APR and APY are not the same
When you borrow or save, two numbers describe the interest: the APR (Annual Percentage Rate) and the APY (Annual Percentage Yield). APR is the headline rate before compounding. APY is what you actually pay or earn after interest is calculated on interest. Because money compounds, APY is always at least as large as APR whenever compounding happens more than once a year. Lenders show APR on loans; banks show APY on savings — each picks the smaller-looking number for their product.
The conversion formulas
APY = (1 + APR/n)n − 1
APR = n × ((1 + APY)1/n − 1)
Here n is the number of compounding periods per year: 365 for daily, 12 for monthly, 4 for quarterly, 1 for annually. The larger n, the bigger the gap between APR and APY.
Worked example
Take a savings account advertising 5% APR compounded monthly. Plug in: APY = (1 + 0.05/12)12 − 1 = 1.004166712 − 1 ≈ 5.116%. Switch to daily compounding and the same 5% APR becomes about 5.127% APY. The nominal rate never changed; only the frequency did. That tiny gap is why comparing APYs directly is the only fair way to shop for deposit accounts.
APR vs APY in the real world
Credit cards usually compound daily, so a 20% APR behaves like roughly a 22% APY on a carried balance — the true cost is higher than the sticker. Mortgages quote APR that already bakes in fees, but the compounding is monthly. Savings and CDs quote APY so you see the real return. Always ask which number you are looking at before signing.
5 tips when comparing rates
- Compare APY to APY. Never pit a loan's APR against a savings APY; they live in different worlds.
- More frequent compounding favors savers. Daily compounding edges out monthly for the same APR.
- Watch "0% APR" teasers. They often revert to a high APY after the promo window, with daily compounding on the balance.
- Annual compounding means APR = APY. If n = 1, the two are identical — no hidden boost either way.
- Use the flip mode for shopping. Enter a competitor's APY and convert it to APR so you can line it up against a quoted APR.
Related calculators
See the same rate math in action with our Compound Interest Calculator, measure a loan's true cost with the Loan Calculator, or project investment growth with the ROI Calculator. Explore the full Finance category.