APR (Annual Percentage Rate) and APY (Annual Percentage Yield) both express yearly interest rates, but APR ignores compounding while APY includes it, making APY always equal to or higher than APR for the same underlying rate. With 12% APR compounded monthly, you earn 1% per month. After one year: (1.01)^12 = 1.1268, meaning 12.68% APY. The more frequent the compounding, the larger the gap: 12% APR compounded daily yields 12.75% APY. With continuous compounding, the formula converges to e^r - 1. DeFi typically quotes APY because blockchain protocols can compound automatically with each block, transaction, or epoch. A lending protocol showing 10% APY means your deposit grows by 10% annually with compounding already factored in. But beware of manipulation: some protocols quote APY assuming unrealistic compounding frequency or based on token emissions that will decline. Always check whether quoted yields are APR or APY and what assumptions underlie the calculation. At low rates the difference is minimal: 5% APR with monthly compounding equals 5.12% APY. At high rates common in DeFi, the gap widens sharply: 100% APR with daily compounding equals 171.5% APY. Understanding this distinction prevents comparing apples to oranges when evaluating yield opportunities across protocols using different conventions.
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