{
  "id": "rule-of-72",
  "version": "9b13e71a96ab",
  "status": "published",
  "name": "Rule of 72 Calculator",
  "question": "What does the rule of 72 say?",
  "summary": "Uses the rule of 72 to estimate how many years money takes to double at a yearly return, or the return that doubles it in a given time, with the exact answer and the rules of 70 and 69.3.",
  "category": "finance",
  "subcategory": "investing",
  "url": "https://www.acalculator.org/finance/rule-of-72-calculator",
  "markdown": "https://www.acalculator.org/finance/rule-of-72-calculator.md",
  "kind": "function",
  "method": "Years ≈ 72 ÷ r and rate ≈ 72 ÷ t (or 70, 69.3). Exact, yearly: t = ln 2 ÷ ln(1 + r/100), r = (2^(1/t) − 1) × 100. Continuous: t = ln 2 ÷ (r/100), r = ln 2 ÷ t × 100.",
  "assumptions": [
    "The rate stays the same every year and all growth is reinvested.",
    "Taxes, fees and inflation are not taken off."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "The years to double at a rate, or the rate that doubles in a number of years.",
        "type": "string",
        "enum": [
          "years",
          "rate"
        ]
      },
      "r": {
        "title": "Yearly rate of return",
        "description": "The yearly interest rate or return, in percent.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0.01,
        "maximum": 100
      },
      "t": {
        "title": "Years to double",
        "description": "The number of years in which the money should double.",
        "type": "number",
        "minimum": 0.1,
        "maximum": 1000
      },
      "rule": {
        "title": "Rule",
        "description": "The number to divide: 72 (the usual rule), 70, or 69.3 (close to continuous compounding).",
        "type": "string",
        "enum": [
          "72",
          "70",
          "69.3"
        ]
      }
    }
  },
  "outputs": {
    "estimate": {
      "label": "Rule estimate",
      "description": "The rule number ÷ the rate (years), or ÷ the years (percent).",
      "format": "number"
    },
    "exact": {
      "label": "Exact, compounded yearly",
      "description": "ln 2 ÷ ln(1 + r) years, or (2^(1/t) − 1) × 100 percent.",
      "format": "number"
    },
    "continuous": {
      "label": "Exact, compounded continuously",
      "description": "ln 2 ÷ r years, or ln 2 ÷ t × 100 percent.",
      "format": "number"
    },
    "difference": {
      "label": "Rule minus exact",
      "description": "The rule estimate minus the yearly-compounding answer.",
      "format": "number"
    },
    "unit": {
      "label": "Answer in",
      "description": "Whether the answers are years or a yearly percent.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "years",
      "r": 9,
      "t": 10,
      "rule": "72"
    },
    "outputs": {
      "estimate": 8,
      "exact": 8.043231726932055,
      "continuous": 7.701635339554948,
      "difference": -0.04323172693205457,
      "unit": "years"
    },
    "text": "By the rule of 72, the answer is about 8 years; exactly 8.04 with yearly compounding."
  },
  "examples": [
    {
      "given": {
        "find": "years",
        "r": 9,
        "rule": "72"
      },
      "expect": {
        "estimate": 8,
        "exact": 8.043231726932055,
        "continuous": 7.701635339554948,
        "unit": "years"
      },
      "source": "SEC, Tips for Teaching Students About Saving and Investing: divide 72 by the expected rate of return; at 9% money doubles about every 8 years, https://www.sec.gov/investor/students/tips.htm; hand calculation in content.mdx: 72 ÷ 9 = 8; ln 2 ÷ ln 1.09 = 8.04"
    },
    {
      "given": {
        "find": "years",
        "r": 6,
        "rule": "72"
      },
      "expect": {
        "estimate": 12,
        "exact": 11.895661045941885,
        "difference": 0.10433895405811455
      },
      "source": "SEC, Tips for Teaching Students About Saving and Investing: divide 72 by the expected rate of return; at 9% money doubles about every 8 years, https://www.sec.gov/investor/students/tips.htm; hand calculation in content.mdx: 72 ÷ 6 = 12; ln 2 ÷ ln 1.06 = 11.90"
    },
    {
      "given": {
        "find": "rate",
        "t": 10,
        "rule": "72"
      },
      "expect": {
        "estimate": 7.2,
        "exact": 7.177346253629316,
        "continuous": 6.931471805599452,
        "unit": "percent a year"
      },
      "source": "SEC, Tips for Teaching Students About Saving and Investing: divide 72 by the expected rate of return; at 9% money doubles about every 8 years, https://www.sec.gov/investor/students/tips.htm; hand calculation in content.mdx: 72 ÷ 10 = 7.2%; (2^0.1 − 1) × 100 = 7.18%"
    },
    {
      "given": {
        "find": "years",
        "r": 7,
        "rule": "70"
      },
      "expect": {
        "estimate": 10,
        "exact": 10.244768351058719
      },
      "source": "SEC, Tips for Teaching Students About Saving and Investing: divide 72 by the expected rate of return; at 9% money doubles about every 8 years, https://www.sec.gov/investor/students/tips.htm (the same rule with 70); hand calculation in content.mdx: 70 ÷ 7 = 10"
    }
  ],
  "sources": [
    "U.S. Securities and Exchange Commission (SEC), Tips for Teaching Students About Saving and Investing: the Rule of 72, divide 72 by the expected rate of return; at 9% an investment doubles about every 8 years. Retrieved 2026-10-02. https://www.sec.gov/investor/students/tips.htm"
  ],
  "related": [
    "compound-interest",
    "investment",
    "cagr",
    "inflation"
  ],
  "changelog": []
}