# APR versus APY: how compounding changes a displayed rate APR commonly expresses a simple annualized rate, while APY includes an assumed compounding effect. Check the interface’s definition before comparing DeFi rates. Compare the calculation method, reward currency, reinvestment frequency and fees; neither label guarantees that a variable rate will persist for a year. Evidence: [Aave Docs Glossary](https://www.aave.com/docs/resources/glossary); [How does compound interest work?](https://www.consumerfinance.gov/ask-cfpb/how-does-compound-interest-work-en-1683/); [Aave V3 MathUtils](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/math/MathUtils.sol); [DefiLlama: How we calculate TVL](https://docs.llama.fi/analysts/data-definitions) Canonical: https://degreesofsatoshi.com/encyclopedia/apr-vs-apy/ Published: 2026-10-02 Substantively modified: 2026-10-02 Independently verified by an automated reviewer: 2026-10-02T18:15:18.493Z Data current through: 2026-10-02 AI-assisted research and drafting with a separate automated source-verification pass; no external expert or named human review is implied. ## Key facts - **Compounding:** Reinvested earnings can themselves earn additional returns. ([How does compound interest work?](https://www.consumerfinance.gov/ask-cfpb/how-does-compound-interest-work-en-1683/)) - **Illustrative formula:** For a fixed nominal rate r compounded n times, annual yield is (1 + r/n)^n − 1. ([How does compound interest work?](https://www.consumerfinance.gov/ask-cfpb/how-does-compound-interest-work-en-1683/)) - **Protocol accounting:** Aave’s cited math library distinguishes linear and approximated compounded-interest calculations. ([Aave V3 MathUtils](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/math/MathUtils.sol)) ## Compare the same principal and assumptions At an illustrative fixed 12% nominal annual rate, monthly compounding gives (1 + 0.12/12)^12 − 1, approximately 12.68%. Without reinvestment, the simple one-year return on unchanged principal is 12%. This arithmetic assumes a fixed rate, successful reinvestment and no costs. It is not a quote from a live pool. Evidence: [How does compound interest work?](https://www.consumerfinance.gov/ask-cfpb/how-does-compound-interest-work-en-1683/) ## Annualization is a projection of a rate or period Lending rates can change with utilization and parameters. Multiplying a short period’s earnings into an annual figure does not establish what later periods will earn. A protocol’s exact index formula can also differ from a dashboard’s display convention. Use the underlying calculation rather than only comparing two large percentages. Evidence: [Reserve](https://www.aave.com/docs/aave-v3/concepts/reserve); [Aave V3 MathUtils](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/math/MathUtils.sol) ## Separate earned assets from displayed reward value A yield display may combine interest, trading fees and token incentives. Rewards denominated in a volatile token add a price assumption when displayed as a dollar percentage. Show fees, reinvestment costs and whether rewards are automatically compounded. A higher headline figure can describe a different set of exposures. Evidence: [DefiLlama: How we calculate TVL](https://docs.llama.fi/analysts/data-definitions) ## Questions ### Does a 20% APY promise a 20% profit over the next year? No. It describes a calculation under stated or implied assumptions. Rates, asset prices, costs and principal losses can change the realized outcome. Evidence: [How does compound interest work?](https://www.consumerfinance.gov/ask-cfpb/how-does-compound-interest-work-en-1683/); [Reserve](https://www.aave.com/docs/aave-v3/concepts/reserve) ## Claims and scope ### apr-vs-apy-quick-answer APR commonly expresses a simple annualized rate, while APY includes an assumed compounding effect. Check the interface’s definition before comparing DeFi rates. Compare the calculation method, reward currency, reinvestment frequency and fees; neither label guarantees that a variable rate will persist for a year. Scope: {"collection":"defi","dataAsOf":"2026-10-02","blockHeight":null} ### apr-vs-apy-fact-compounding Compounding: Reinvested earnings can themselves earn additional returns. Scope: {"collection":"defi","dataAsOf":"2026-10-02","blockHeight":null} ### apr-vs-apy-fact-illustrative-formula Illustrative formula: For a fixed nominal rate r compounded n times, annual yield is (1 + r/n)^n − 1. Scope: {"collection":"defi","dataAsOf":"2026-10-02","blockHeight":null} ### apr-vs-apy-fact-protocol-accounting Protocol accounting: Aave’s cited math library distinguishes linear and approximated compounded-interest calculations. Scope: {"collection":"defi","dataAsOf":"2026-10-02","blockHeight":null} ## Sources - [Aave Docs Glossary](https://www.aave.com/docs/resources/glossary) — Aave. Protocol glossary distinguishes APY including compounding from APR and defines lending terms. Locator: APY; Borrow Cap; Credit Delegation; Debt Ceiling. Retrieved: 2026-10-02T17:58:05.650Z. - [How does compound interest work?](https://www.consumerfinance.gov/ask-cfpb/how-does-compound-interest-work-en-1683/) — Consumer Financial Protection Bureau. The arithmetic effect of compounding at a stated hypothetical rate. Locator: Compound interest; Examples. Retrieved: 2026-10-02T17:21:46.950Z. - [Aave V3 MathUtils](https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/math/MathUtils.sol) — Aave. Protocol-specific simple and approximated compounded interest calculations. Locator: calculateLinearInterest; calculateCompoundedInterest. Retrieved: 2026-10-02T17:03:44.337Z. - [DefiLlama: How we calculate TVL](https://docs.llama.fi/analysts/data-definitions) — DefiLlama. Provider-specific valuation scope and TVL methodology. Locator: Total Value Locked. Retrieved: 2026-10-02T17:03:46.209Z. - [Reserve](https://www.aave.com/docs/aave-v3/concepts/reserve) — Aave. Reserve LTV, liquidation threshold, borrow availability, caps and rate parameters. Locator: Key Reserve Parameters; Dynamic Parameters and Governance. Retrieved: 2026-10-02T17:03:44.647Z. ## Revision history - 2026-10-02: First publication after primary-source research and independent automated verification. ## Cite this entry Degrees of Satoshi editorial project. “APR versus APY: how compounding changes a displayed rate.” Published 2026-10-02; updated 2026-10-02. https://degreesofsatoshi.com/encyclopedia/apr-vs-apy/