APR vs APY Calculator

Type an APR with a compounding frequency (monthly, daily, continuous) and the calculator returns the equivalent APY — the rate you actually earn or pay after compounding. Or go the other direction: type an APY and back-solve for the APR.

APY is always higher than APR when compounding is more frequent than annual. The gap matters most at high rates and high frequencies — a 12% APR compounded daily is 12.747% APY; the same APR compounded annually is just 12%. On a credit card balance over years, that 0.747% spread compounds further into real money.

For savings, APY is the honest figure. For loans, APR is the honest figure (it includes fees that APY ignores). Lenders quote whichever number is more flattering, which is why both exist as marketing terms.

The formula: APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. n=12 for monthly, n=365 for daily, n=∞ (continuous compounding) gives APY = e^APR − 1. The calculator runs all three and shows which assumption your bank or lender uses. Daily compounding is standard for credit cards and high-yield savings; monthly is standard for most mortgages and fixed-rate loans. Continuous is rare in retail — mostly an academic / quant-finance construct.

Worked example: a credit card quotes 24% APR. With daily compounding (most cards), APY = (1 + 0.24/365)^365 − 1 = 27.11%. So a $5,000 balance carried for one year at the minimum payment costs ~$1,355 in interest, not $1,200. Across two years: $5,000 × 1.2711^2 ≈ $8,078, meaning interest alone over that period is over $3,000. The APR-vs-APY gap doesn't sound large until you do this math on a real balance.

The direction the marketing tilts: banks quote APY for deposits (the higher-looking number; 5.0% APY makes a savings account sound better than 4.879% APR with daily compounding). Lenders quote APR for loans (the lower-looking number; 6.5% APR sounds friendlier than 6.7% APY). When comparing, normalize. Ask the bank: 'What's the APY?' and the lender: 'What's the APR including fees?' The honest comparison metric is the same on both sides: total dollars in your pocket vs out of it over the same period.

Adjacent concepts to know: effective interest rate (same as APY in most usage), nominal rate (same as APR), real rate (APR minus inflation — what your money actually grows in purchasing power). For a savings account at 5% APY when inflation is 3%, your real return is roughly 2%. That's the figure that determines whether savings actually preserve value over time, and it's a number nobody quotes because it's almost always lower than the nominal.