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  "id": "apr-vs-apy",
  "canonical": "https://degreesofsatoshi.com/encyclopedia/apr-vs-apy/",
  "collection": "defi",
  "title": "APR versus APY: how compounding changes a displayed rate",
  "description": "Compare a simple annualized rate with a compounded annual yield, using explicit assumptions about reinvestment, variable rates, fees and reward-token prices.",
  "aliases": [
    "APR",
    "APY"
  ],
  "dates": {
    "published": "2026-10-02",
    "modified": "2026-10-02",
    "verified": "2026-10-02T18:15:18.493Z",
    "dataAsOf": "2026-10-02"
  },
  "authorship": {
    "publisher": "Degrees of Satoshi editorial project",
    "process": "AI-assisted research and drafting with a separate automated source-verification pass; no external expert or named human review is implied."
  },
  "quickAnswer": {
    "text": "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.",
    "claimId": "apr-vs-apy-quick-answer",
    "sourceIds": [
      "aave-glossary",
      "investor-compound",
      "aave-math",
      "defillama-tvl"
    ]
  },
  "keyFacts": [
    {
      "label": "Compounding",
      "value": "Reinvested earnings can themselves earn additional returns.",
      "sourceIds": [
        "investor-compound"
      ],
      "id": "compounding",
      "claimId": "apr-vs-apy-fact-compounding"
    },
    {
      "label": "Illustrative formula",
      "value": "For a fixed nominal rate r compounded n times, annual yield is (1 + r/n)^n − 1.",
      "sourceIds": [
        "investor-compound"
      ],
      "id": "illustrative-formula",
      "claimId": "apr-vs-apy-fact-illustrative-formula"
    },
    {
      "label": "Protocol accounting",
      "value": "Aave’s cited math library distinguishes linear and approximated compounded-interest calculations.",
      "sourceIds": [
        "aave-math"
      ],
      "id": "protocol-accounting",
      "claimId": "apr-vs-apy-fact-protocol-accounting"
    }
  ],
  "prerequisites": [
    "stablecoin-yield-sources"
  ],
  "sections": [
    {
      "id": "example",
      "heading": "Compare the same principal and assumptions",
      "sourceIds": [
        "investor-compound"
      ],
      "paragraphs": [
        "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."
      ]
    },
    {
      "id": "variable",
      "heading": "Annualization is a projection of a rate or period",
      "sourceIds": [
        "aave-reserve",
        "aave-math"
      ],
      "paragraphs": [
        "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."
      ]
    },
    {
      "id": "net",
      "heading": "Separate earned assets from displayed reward value",
      "sourceIds": [
        "defillama-tvl"
      ],
      "paragraphs": [
        "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."
      ]
    }
  ],
  "faq": [
    {
      "question": "Does a 20% APY promise a 20% profit over the next year?",
      "answer": "No. It describes a calculation under stated or implied assumptions. Rates, asset prices, costs and principal losses can change the realized outcome.",
      "sourceIds": [
        "investor-compound",
        "aave-reserve"
      ]
    }
  ],
  "claims": [
    {
      "id": "apr-vs-apy-quick-answer",
      "articleSlug": "apr-vs-apy",
      "statement": "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.",
      "sourceIds": [
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      "sourceLocators": [
        {
          "sourceId": "source-8847a72e1c4b461f",
          "locator": "APY; Borrow Cap; Credit Delegation; Debt Ceiling"
        },
        {
          "sourceId": "source-f6fab0de28f98515",
          "locator": "Compound interest; Examples"
        },
        {
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          "locator": "calculateLinearInterest; calculateCompoundedInterest"
        },
        {
          "sourceId": "source-3649ada489ba8078",
          "locator": "Total Value Locked"
        }
      ],
      "scope": {
        "collection": "defi",
        "dataAsOf": "2026-10-02",
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      "qualification": "",
      "evidenceStatus": "documented",
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        "checkedAt": "2026-10-02T18:15:18.493Z",
        "reviewer": "automated independent verification — DeFi expansion reviewer",
        "notes": [
          "Added Aave glossary for the direct APR/APY distinction; the CFPB page supports compounding, not the original terminology claim. Replaced unsupported claim about inconsistent interface labels with an instruction to check definitions.",
          "Recomputed (1+0.12/12)^12-1 = 0.12682503013196977, or 12.68%. The key-fact formula is an explicitly illustrative derivation from repeated compounding. Compared MathUtils linear and binomial compounded implementations at v1.19.3; no promise of a fixed live rate."
        ]
      }
    },
    {
      "id": "apr-vs-apy-fact-compounding",
      "articleSlug": "apr-vs-apy",
      "statement": "Compounding: Reinvested earnings can themselves earn additional returns.",
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        "notes": [
          "Added Aave glossary for the direct APR/APY distinction; the CFPB page supports compounding, not the original terminology claim. Replaced unsupported claim about inconsistent interface labels with an instruction to check definitions.",
          "Recomputed (1+0.12/12)^12-1 = 0.12682503013196977, or 12.68%. The key-fact formula is an explicitly illustrative derivation from repeated compounding. Compared MathUtils linear and binomial compounded implementations at v1.19.3; no promise of a fixed live rate."
        ]
      }
    },
    {
      "id": "apr-vs-apy-fact-illustrative-formula",
      "articleSlug": "apr-vs-apy",
      "statement": "Illustrative formula: For a fixed nominal rate r compounded n times, annual yield is (1 + r/n)^n − 1.",
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        "source-f6fab0de28f98515"
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          "locator": "Compound interest; Examples"
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        "notes": [
          "Added Aave glossary for the direct APR/APY distinction; the CFPB page supports compounding, not the original terminology claim. Replaced unsupported claim about inconsistent interface labels with an instruction to check definitions.",
          "Recomputed (1+0.12/12)^12-1 = 0.12682503013196977, or 12.68%. The key-fact formula is an explicitly illustrative derivation from repeated compounding. Compared MathUtils linear and binomial compounded implementations at v1.19.3; no promise of a fixed live rate."
        ]
      }
    },
    {
      "id": "apr-vs-apy-fact-protocol-accounting",
      "articleSlug": "apr-vs-apy",
      "statement": "Protocol accounting: Aave’s cited math library distinguishes linear and approximated compounded-interest calculations.",
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      "sourceLocators": [
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          "locator": "calculateLinearInterest; calculateCompoundedInterest"
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          "Added Aave glossary for the direct APR/APY distinction; the CFPB page supports compounding, not the original terminology claim. Replaced unsupported claim about inconsistent interface labels with an instruction to check definitions.",
          "Recomputed (1+0.12/12)^12-1 = 0.12682503013196977, or 12.68%. The key-fact formula is an explicitly illustrative derivation from repeated compounding. Compared MathUtils linear and binomial compounded implementations at v1.19.3; no promise of a fixed live rate."
        ]
      }
    }
  ],
  "sources": [
    {
      "id": "aave-glossary",
      "label": "Aave Docs Glossary",
      "publisher": "Aave",
      "url": "https://www.aave.com/docs/resources/glossary",
      "locator": "APY; Borrow Cap; Credit Delegation; Debt Ceiling",
      "note": "Protocol glossary distinguishes APY including compounding from APR and defines lending terms.",
      "version": null,
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      "id": "investor-compound",
      "label": "How does compound interest work?",
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      "url": "https://www.consumerfinance.gov/ask-cfpb/how-does-compound-interest-work-en-1683/",
      "locator": "Compound interest; Examples",
      "note": "The arithmetic effect of compounding at a stated hypothetical rate.",
      "version": null,
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      "url": "https://raw.githubusercontent.com/aave/aave-v3-core/v1.19.3/contracts/protocol/libraries/math/MathUtils.sol",
      "locator": "calculateLinearInterest; calculateCompoundedInterest",
      "note": "Protocol-specific simple and approximated compounded interest calculations.",
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    {
      "id": "defillama-tvl",
      "label": "DefiLlama: How we calculate TVL",
      "publisher": "DefiLlama",
      "url": "https://docs.llama.fi/analysts/data-definitions",
      "locator": "Total Value Locked",
      "note": "Provider-specific valuation scope and TVL methodology.",
      "version": null,
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      "label": "Reserve",
      "publisher": "Aave",
      "url": "https://www.aave.com/docs/aave-v3/concepts/reserve",
      "locator": "Key Reserve Parameters; Dynamic Parameters and Governance",
      "note": "Reserve LTV, liquidation threshold, borrow availability, caps and rate parameters.",
      "version": "Aave V3 documentation",
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  "related": {
    "articles": [
      "realized-vs-projected-yield",
      "token-emission-dilution",
      "incentives-and-earned-fees"
    ],
    "dossiers": [],
    "wallets": []
  },
  "revisionHistory": [
    {
      "date": "2026-10-02",
      "kind": "published",
      "summary": "First publication after primary-source research and independent automated verification."
    }
  ],
  "citation": "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/"
}