{
  "id": "effective-interest-rate",
  "version": "c9b3c4cd324a",
  "status": "published",
  "name": "Effective Interest Rate Calculator",
  "question": "What is my effective interest rate?",
  "summary": "Converts a stated (nominal) interest rate to its effective annual rate for daily, monthly, quarterly, twice-yearly, yearly or continuous compounding, and back.",
  "category": "finance",
  "subcategory": "investing",
  "url": "https://www.acalculator.org/finance/effective-interest-rate-calculator",
  "markdown": "https://www.acalculator.org/finance/effective-interest-rate-calculator.md",
  "kind": "formulas",
  "method": "EAR = (1 + r ÷ n)^n − 1, where r is the stated yearly rate and n the times interest is compounded a year; EAR = e^r − 1 for continuous compounding. Back: r = n × ((1 + EAR)^(1/n) − 1), or ln(1 + EAR).",
  "assumptions": [
    "The stated rate stays the same for the whole year, and interest is added to the balance at each compounding.",
    "Daily compounding uses 365 days a year.",
    "No fees. For a savings account the effective annual rate is the annual percentage yield (APY)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "rate": {
        "title": "Stated interest rate",
        "description": "The nominal yearly interest rate before compounding (the rate quoted, or the APR for a loan).",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 100
      },
      "ear": {
        "title": "Effective annual rate (EAR)",
        "description": "The rate actually earned or paid in a year once compounding is counted, as a percent.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 200
      },
      "comp": {
        "title": "Interest is compounded",
        "description": "How often interest is added to the balance: daily (365 times a year), monthly, quarterly, twice a year, yearly or continuously.",
        "type": "string",
        "enum": [
          "365",
          "12",
          "4",
          "2",
          "1",
          "continuous"
        ]
      }
    }
  },
  "solve": {
    "fillAny": 1,
    "variables": [
      "rate",
      "ear"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "rate": {
      "label": "Stated interest rate",
      "description": "The nominal yearly interest rate before compounding (the rate quoted, or the APR for a loan).",
      "format": "percent"
    },
    "ear": {
      "label": "Effective annual rate (EAR)",
      "description": "The rate actually earned or paid in a year once compounding is counted, as a percent.",
      "format": "percent"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "comp": "12",
      "rate": 6
    },
    "outputs": {
      "ear": 6.1677811864499565
    },
    "text": "A stated rate of 6% compounded monthly is an effective annual rate of 6.168%."
  },
  "examples": [
    {
      "given": {
        "rate": 6,
        "comp": "12"
      },
      "expect": {
        "ear": 6.1677811864499565
      },
      "source": "Regulation DD (Truth in Savings), 12 CFR part 1030, appendix A, Part I ($61.68 of interest on $1,000 for a 365-day year is an annual percentage yield of 6.17%). https://www.law.cornell.edu/cfr/text/12/appendix-A_to_part_1030, retrieved 2026-10-02; hand calculation in content.mdx: (1 + 0.06/12)^12 − 1 = 6.1678%"
    },
    {
      "given": {
        "rate": 12,
        "comp": "4"
      },
      "expect": {
        "ear": 12.550881
      },
      "source": "hand calculation in content.mdx: (1 + 0.12/4)^4 − 1 = 1.03^4 − 1 = 12.5509%"
    },
    {
      "given": {
        "rate": 18,
        "comp": "365"
      },
      "expect": {
        "ear": 19.716424499274456
      },
      "source": "hand calculation in content.mdx: (1 + 0.18/365)^365 − 1 = 19.7164%"
    },
    {
      "given": {
        "ear": 10,
        "comp": "12"
      },
      "expect": {
        "rate": 9.568968514684489
      },
      "source": "hand calculation in content.mdx: 12 × (1.10^(1/12) − 1) = 9.5690%"
    },
    {
      "given": {
        "rate": 5,
        "comp": "continuous"
      },
      "expect": {
        "ear": 5.127109637602404
      },
      "source": "hand calculation in content.mdx: e^0.05 − 1 = 5.1271%"
    }
  ],
  "sources": [
    "Regulation DD (Truth in Savings), 12 CFR part 1030, appendix A, Part I: annual percentage yield = 100 [(1 + Interest/Principal)^(365/Days in term) − 1]; $61.68 of interest on $1,000 over 365 days is 6.17%. https://www.law.cornell.edu/cfr/text/12/appendix-A_to_part_1030 (retrieved 2026-10-02)",
    "Consumer Financial Protection Bureau, Regulation DD, 12 CFR 1030.2: definition of annual percentage yield. https://www.consumerfinance.gov/rules-policy/regulations/1030/2/ (retrieved 2026-10-02)"
  ],
  "related": [
    "apy",
    "apr",
    "compound-interest",
    "interest-rate"
  ],
  "changelog": []
}