Effective Annual Rate Explained: The Number That Actually Matters

APR, APY, and effective annual rate (EAR) all describe the same underlying thing — what interest costs or earns over a year — but they account for compounding differently. Mixing them up is one of the most common ways to misjudge a financial product.

APR: Annual Percentage Rate

APR is the nominal rate, not adjusted for intra-year compounding. A 12% APR credit card with monthly compounding actually charges 12.68% in real-world annual interest. APR is what loan disclosures show — useful for comparing loans, misleading for comparing savings accounts.

APY: Annual Percentage Yield

APY (a.k.a. EAR, Effective Annual Rate) accounts for compounding within the year. Formula: APY = (1 + r/n)^n - 1, where r is the APR and n is the compounding periods per year. APY is the honest number for savings accounts and the only valid way to compare them.

Worked translation example

A money-market account advertises 5% APR compounded daily. APY = (1 + 0.05/365)^365 - 1 = 5.127%. A different bank advertises 5.1% APY. The first bank is actually paying 0.027% more — but a casual shopper might assume the 5.1% APY is better than the 5% APR.

Why the gap grows with compounding frequency

• Annual compounding: APR = APY exactly.
• Semi-annual: APY is 0.06% higher than APR at 5%.
• Quarterly: APY is 0.09% higher.
• Monthly: APY is 0.12% higher.
• Daily: APY is 0.13% higher.
• Continuous: APY is 0.13% higher (the mathematical limit).

The rule for shoppers

Compare savings accounts on APY. Compare loans on APR (since loan APR already includes most fees by law). Never compare a savings APR to a loan APY — you're mixing units. If a product quotes only the rate without 'APR' or 'APY,' assume it's whichever is more favorable to them, and ask for clarification.

Inflation-adjusted ('real') return

The most honest rate of all is real return — your APY minus inflation. A 4.5% APY savings account in 3% inflation has a 1.5% real return. Investing returns should usually be expressed in real terms (7% real for stocks) so projections make sense in today's purchasing power.