APR vs APY — What's the difference?
Annual Percentage Rate (APR) is the stated interest rate without accounting for compounding within the year. Annual Percentage Yield (APY) — also called the Effective Annual Rate (EAR) — reflects the actual return after compounding is applied. The more frequently interest compounds, the wider the gap between APR and APY.
For savings accounts and investments, APY is what you actually earn. For loans and credit cards, lenders often advertise APR — the true cost is higher once compounding is factored in. This calculator converts between the two so you're always comparing apples to apples.
The formula
APY is derived from APR using the following formula, where n is the number of compounding periods per year:
APY = (1 + APRn)ⁿ − 1
The intuition: each compounding period, interest is earned on previously earned interest. The more periods per year, the more times this snowballing effect occurs.
Worked example: A savings account advertises 5% APR compounded monthly (n = 12).
APY = (1 + 0.0512)¹² − 1 = (1.004167)¹² − 1 ≈ 5.116%
On a $10,000 deposit held for one year, the difference is $11.60 — not life-changing, but it compounds meaningfully over time and matters when comparing accounts at scale.
When the difference actually matters
The APR/APY gap is small at low rates and widens significantly at higher ones. Here's where it has real practical impact:
- High-yield savings accounts: Banks are required by the Truth in Savings Act to disclose APY, but when comparing international or fintech offers, you may only see APR. Always convert before comparing.
- Credit cards: A card with a 24% APR compounded daily has an APY of about 27.1%. That's the true annualized cost if you carry a balance month to month.
- Mortgages: Mortgage APR often includes fees (origination, points), making it higher than the note rate. It's not directly convertible using this formula — but it's still more useful than the raw rate for comparing loan offers.
- Certificates of deposit: CDs with the same APR but different compounding frequencies (monthly vs. quarterly) will have different APYs. The one compounding more frequently always wins.
Common mistakes
- Comparing APR to APY directly: Seeing "5% APR" at one bank and "5.1% APY" at another doesn't mean the second is better — they're measuring different things. Convert both to APY first.
- Assuming APR = interest rate on loans: For mortgages and auto loans in the U.S., the disclosed APR includes fees and is higher than the actual interest rate. It's a cost comparison tool, not a direct input to this formula.
- Forgetting continuous compounding: At the limit where compounding frequency approaches infinity, APY = e^APR − 1, where e ≈ 2.718. Some money market instruments use continuous compounding — daily compounding is a very close approximation but not identical.
How to use this calculator
Enter the nominal APR and the compounding frequency (12 = monthly, 365 = daily, 4 = quarterly). The calculator returns the effective APY. Use it when comparing savings account offers, evaluating loan costs, or converting between rate formats on financial statements.
Frequently Asked Questions
Is APY always higher than APR?
Yes, as long as compounding occurs more than once per year. With annual compounding, APY equals APR. With daily compounding, a 5% APR becomes approximately 5.13% APY. The difference grows larger at higher rates and more frequent compounding.
What compounding frequency is most common?
High-yield savings accounts and money market accounts typically compound daily. CDs often compound daily or monthly. Bonds usually compound semi-annually. Credit cards compound daily. Always check the terms — lenders are required to disclose the APY in the U.S. under the Truth in Savings Act.
How is APY calculated from APR?
APY = (1 + APRn)ⁿ − 1, where n is the number of compounding periods per year. For example, 6% APR compounded monthly: (1 + 0.0612)¹² − 1 = (1.005)¹² − 1 ≈ 6.168% APY.
Why do banks advertise APY on savings but APR on loans?
It's a marketing convention. APY sounds higher on savings accounts (good for the bank's pitch), while APR sounds lower on loans (also good for the bank's pitch). As a consumer, always convert to APY to make accurate comparisons — this calculator does exactly that.