What Is APR vs APY and Why Your Savings Account Earns Less Than You Think
APR and APY are not the same. APR ignores compounding; APY includes it. The math, the 5% savings example, and how to compare offers properly.
<strong>APR</strong> is the annual rate without compounding. <strong>APY</strong> is the annual rate with compounding baked in. For a 5% APR compounded daily, the APY is about 5.13% — a 13 basis point gap. The higher the rate or the more frequent the compounding, the wider the gap. The <a href="/compound-interest-calculator">Uttir Compound Interest Calculator</a> runs both sides so you can compare offers.
If you have compared two savings accounts or two credit card offers, you have seen both APR and APY in the fine print. They are not interchangeable. APR is the rate without compounding; APY is the rate with compounding. The two numbers can differ by 13 basis points on a 5% savings account, by 30+ basis points on a credit card with daily compounding, and by far more for high-rate promotional offers.
This post walks through what each one means, why the gap exists, and how to compare offers properly.
What APR is
APR (Annual Percentage Rate) is the annual interest rate, expressed as a simple annualized number, without any compounding inside the year.
So a 5% APR on a $10,000 loan for 1 year charges 5% × $10,000 = $500 in interest over the year, regardless of when the payments are made.
For a credit card, the APR is what the issuer quotes in the Schumer box. The card uses a daily periodic rate (APR ÷ 365) to compute interest each day, and then compounds those daily charges. The result is that the effective rate you actually pay is higher than the APR — sometimes by 13+ basis points at 5%, by 50+ basis points at 18%, and by more at higher rates.
What APY is
APY (Annual Percentage Yield) is the effective annual rate, with compounding included. It is the number you actually earn (or pay) over a year, expressed as a single percentage.
For a 5% APR compounded daily, the APY is:
APY = (1 + 0.05/365)^365 - 1 = 0.05127 = 5.127%So $10,000 at 5.127% APY earns $512.67 in interest over the year, not the $500 the APR would suggest. The extra $12.67 is the compounding.
For a savings account, the APY is the right number to compare across banks. For a credit card, the APY is the effective cost of carrying a balance — and the right number to compare across cards.
Why the gap exists
The gap is purely a function of compounding frequency. The math:
| Compounding | Formula | 5% APR → APY |
|---|---|---|
| Annual (1×/year) | (1 + r/1)^1 - 1 | 5.000% |
| Semiannual (2×/year) | (1 + r/2)^2 - 1 | 5.063% |
| Quarterly (4×/year) | (1 + r/4)^4 - 1 | 5.095% |
| Monthly (12×/year) | (1 + r/12)^12 - 1 | 5.116% |
| Daily (365×/year) | (1 + r/365)^365 - 1 | 5.127% |
| Continuous | e^r - 1 | 5.127% |
The gap widens fast as the rate goes up:
| APR | APY (daily) | Gap |
|---|---|---|
| 2% | 2.020% | 2.0 bps |
| 5% | 5.127% | 12.7 bps |
| 10% | 10.516% | 51.6 bps |
| 18% | 19.716% | 171.6 bps |
| 25% | 28.393% | 339.3 bps |
At credit-card rates, the gap is meaningful. At a 25% APR card with daily compounding, the APY is 28.4% — the difference between owing $2,500 in interest and $2,840 in interest on a $10,000 balance over a year.
What to look at when comparing offers
- For savings accounts, CDs, money market accounts: always compare APY. The bank is required to quote the APY by federal law (US Truth in Savings Act, EU consumer credit rules).
- For credit cards: compare APR for the headline rate, then mentally convert to APY if you carry a balance. The 13-50 bps gap matters at high rates.
- For mortgages: the APR is a slightly different number (it includes some closing costs), but the comparable rate is the note rate (the rate the lender quotes on the loan itself). Compare the note rate for a clean comparison; use the APR to compare total cost including closing costs.
- For personal loans and auto loans: the APR is the right number, since these loans do not compound inside the year.
Common mistakes
- Comparing APR to APY. The two are not interchangeable. Always convert to the same number before comparing offers.
- Ignoring compounding frequency. “5% compounded daily” earns more than “5% compounded monthly.” For the same APR, daily is the most generous for savers and the most expensive for borrowers.
- Trusting the headline APR for promotional rates. Credit card “0% APR for 18 months” is real, but the post-promo APR is typically 22-29% — and the daily compounding from the start means the moment the promo ends, you start paying 22%+ APY on whatever balance is left.
- Confusing the savings account APY with the CD APY. A 12-month CD and a savings account may have the same APY on day 1, but the CD locks you in, and the early-withdrawal penalty can be 3-6 months of interest.
How to compare offers properly
For any offer — savings, CD, credit card, loan — convert everything to APY first, then compare on the same basis. The Uttir Compound Interest Calculator runs both sides: enter the APR, the compounding frequency, and the principal; it returns the year-end balance and the effective APY. For a 5% APR savings account compounded daily, you will see the $10,000 grow to $10,512.67 in a year, with the APY listed as 5.127%.
For the inflation side of the question (is 5% APY really 5% in real terms?), the Uttir Inflation Calculator is the right tool. For the loan side, the Uttir Mortgage Calculator and Loan Calculator cover the financing math.
Bottom line
APR is the rate, APY is what you actually earn or pay after compounding. For a 5% savings account the gap is 13 bps; for a 25% credit card the gap is 339 bps. Always compare APY to APY. The Uttir Compound Interest Calculator does the conversion in your browser, no upload, no signup.