APR
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APY
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Daily Rate
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Monthly Rate
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Effective Annual Rate
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Doubles In (Rule of 72)
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APR vs APY — What's the Difference?
APR (Annual Percentage Rate) is the stated or nominal interest rate for a year, without taking compounding into account. It's what lenders advertise.
APY (Annual Percentage Yield) is the effective annual rate that accounts for how often interest compounds within the year. It's always equal to or greater than APR, and represents what you actually earn (or pay) over a year.
The key rule: for savings accounts, banks advertise APY (it's the higher number — better marketing). For loans, lenders advertise APR (it's the lower number — looks cheaper). Always compare accounts using the same metric.
The Conversion Formulas
APY = (1 + APR/n)ⁿ − 1
n = number of compounding periods per year
APR = n × ((1 + APY)^(1/n) − 1)
Reverse conversion from APY back to APR
APY = e^(APR) − 1 (continuous compounding)
e = Euler's number (≈ 2.71828) — used when interest compounds continuously
Quick Reference
Savings Accounts / CDs
Banks advertise APY. Use APY to compare accounts — it tells you exactly what you'll earn in a year regardless of compounding frequency.
Credit Cards
Cards advertise APR but compound daily (365×/year). A 24% APR credit card has an effective APY of ~26.97% — significantly higher.
Mortgages & Auto Loans
APR on these loans also includes fees (origination, points), making it a more complete cost measure. Always compare mortgage offers by APR.
Crypto / DeFi Yields
DeFi protocols often advertise APY assuming continuous compounding and reinvestment. Actual yields depend heavily on reinvestment frequency — use our compound interest calculator to verify.
Frequently Asked Questions
Why is APY always higher than APR?
Because compounding adds interest on top of previously earned interest. When interest compounds more than once per year, you effectively earn a return on your returns. The only exception is when compounding occurs once per year (n=1), in which case APY = APR exactly. The more frequently interest compounds, the larger the gap between APR and APY.
Does compounding frequency matter much in practice?
For savings accounts, the difference between daily and monthly compounding is small — on $10,000 at 5% APR, daily compounding earns about $1.30 more per year than monthly. However, the compounding frequency matters enormously for the rate you're advertised. A savings account advertising 5% APY with monthly compounding has an actual APR of 4.889% — that's what matters when comparing to a bond or CD that uses a different convention.
What is continuous compounding?
Continuous compounding is the mathematical limit of compounding infinitely frequently. It uses the formula APY = e^(APR) − 1, where e ≈ 2.71828. In practice, no account truly compounds continuously — it's a theoretical maximum. Some financial models use it for simplicity. A 5% APR with continuous compounding yields an APY of 5.127% — slightly higher than daily compounding at 5.126%.
Which should I use when comparing savings accounts?
Always compare savings accounts using APY. APY already accounts for compounding frequency, so a 5% APY account with daily compounding and a 5% APY account with monthly compounding will earn exactly the same amount in a year on the same balance. APY is the true apples-to-apples comparison metric for savings. By law, US banks are required to disclose APY for deposit accounts under the Truth in Savings Act.