{
  "address": "035b0d84792e2c80de55d6a3f7c5cbee",
  "category": "other",
  "question": "What is the effective annual rate (APY) of a nominal annual rate of 12% compounded 12 times per year?",
  "answer": "12.68%",
  "askedBy": {
    "kind": "guest",
    "display": "method deck",
    "stamped": false,
    "id": null
  },
  "answeredBy": "method",
  "madeAt": "2026-09-30T22:39:30.722Z",
  "validUntil": null,
  "validityClass": "forever",
  "sources": [
    {
      "label": "Principles of Corporate Finance",
      "url": null
    }
  ],
  "supersedes": null,
  "supersededBy": null,
  "isSeed": false,
  "seedSource": null,
  "seedAttribution": null,
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  "unpublishedAt": null,
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  "queuedForSubstrate": false,
  "answerMethod": "method",
  "unsourced": false,
  "source": {
    "kind": "edition_page",
    "value": "Brealey, Myers, Allen, Principles of Corporate Finance, 13th ed., Chapter 3, section on compounding intervals and the effective annual rate",
    "retrieved_utc": "2026-09-30T19:31:29Z"
  },
  "qsha256": "b4d80bf38b4917aff499031c2f16ac156b0991dfe525c6a892de7fc08c8de54d",
  "runOne": null,
  "cardContractVersion": "card_contract/1",
  "deck_id": "method-deck",
  "deck_title": "Method Deck",
  "method": {
    "name": "APR to APY (effective annual rate)",
    "version": "1",
    "source_url_or_file": "methods/apr-to-apy.cjs",
    "sha256_of_method_file": "f3b0995a9d6d3d74550a8a7f13f03b4cbbef7ba31a2b6b9111a9aec73f94bee6"
  },
  "receipt": {
    "inSubstrate": false,
    "local": true,
    "modelCallsAtMint": 0,
    "tokensAtMint": 0
  },
  "method_deck": {
    "inputs": [
      {
        "name": "nominal_annual_rate_percent",
        "type": "number",
        "unit": "%",
        "required": true,
        "description": "Nominal annual rate (APR)",
        "min": 0
      },
      {
        "name": "compounds_per_year",
        "type": "integer",
        "required": true,
        "description": "Number of compounding periods per year",
        "enum": [
          1,
          2,
          4,
          12,
          52,
          365
        ]
      }
    ],
    "outputs": [
      {
        "name": "effective_annual_rate_percent",
        "unit": "%",
        "description": "Effective annual rate (APY)"
      }
    ],
    "steps": [
      "Convert the nominal rate to a decimal: r = nominal_annual_rate_percent / 100.",
      "Periodic rate i = r / compounds_per_year.",
      "APY as a decimal = (1 + i) ^ compounds_per_year - 1.",
      "effective_annual_rate_percent = APY * 100, rounded to 4 decimals for display as a percent with 2 shown."
    ],
    "constants": [],
    "examples": [
      {
        "name": "worked example",
        "inputs": {
          "nominal_annual_rate_percent": 12,
          "compounds_per_year": 12
        },
        "expected": {
          "answer": "12.68%"
        },
        "check": "hand computation: i = 0.01, APY = (1.01)^12 - 1 = 0.126825..., 12.6825% rounds to 12.68%"
      },
      {
        "name": "test vector: quarterly compounding",
        "inputs": {
          "nominal_annual_rate_percent": 6,
          "compounds_per_year": 4
        },
        "expected": {
          "answer": "6.14%"
        },
        "check": "hand computation: i = 0.015, APY = (1.015)^4 - 1 = 0.061364..., 6.1364% rounds to 6.14%"
      }
    ],
    "disclaimer": null,
    "deck_category": "finance"
  },
  "status": "minted",
  "kind": "method",
  "provenanceClass": "own_question",
  "provenance": {
    "schema": "card_provenance/2.0.0",
    "chain": [
      {
        "source": {
          "kind": "edition_page",
          "value": "Brealey, Myers, Allen, Principles of Corporate Finance, 13th ed., Chapter 3, section on compounding intervals and the effective annual rate",
          "retrieved_utc": "2026-09-30T19:31:29Z"
        },
        "sha256": "8059eec1fa93c2c4febd435be5d44f4d8099c41f8f82b380090a735234eee218",
        "supersedes": null,
        "added_utc": "2026-09-30T22:39:30.722Z",
        "added_by": "method:APR to APY (effective annual rate)",
        "why": "the method that computed this answer",
        "check": null,
        "status_label": "pending",
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      }
    ]
  }
}