{
  "id": "index-fund",
  "version": "c7a4bf92289b",
  "status": "published",
  "name": "Index Fund Calculator",
  "question": "What will my index fund grow to?",
  "summary": "Computes the growth of an index fund investment with monthly additions at an expected return after its expense ratio, and how much more it keeps than a fund with a higher expense ratio.",
  "category": "finance",
  "subcategory": "investing",
  "url": "https://www.acalculator.org/finance/index-fund-calculator",
  "markdown": "https://www.acalculator.org/finance/index-fund-calculator.md",
  "kind": "schedule",
  "method": "Each month: value × (1 + R)^(1/12), less a twelfth of the expense ratio on that, plus the monthly addition; the comparison fund runs the same with its own expense ratio.",
  "assumptions": [
    "The index return is the same every year; real index returns go up and down, and past returns do not predict future ones.",
    "Additions are made at the end of each month.",
    "Taxes, trading costs and tracking error are not included. This is an estimate, not investment advice."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "initial": {
        "title": "Initial investment",
        "description": "The amount you invest at the start.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 1000000000
      },
      "monthly": {
        "title": "Added each month",
        "description": "An amount invested at the end of every month. Leave it empty or 0 for none.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 100000000
      },
      "ret": {
        "title": "Expected return (yearly)",
        "description": "The yearly return of the index before the fund’s expenses. Type your own estimate.",
        "type": "number",
        "x-unit": "percent",
        "minimum": -50,
        "maximum": 50
      },
      "er": {
        "title": "Expense ratio",
        "description": "The index fund’s annual expense ratio, from its prospectus or fact sheet.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 5
      },
      "years": {
        "title": "Years",
        "description": "How many years you stay invested.",
        "type": "integer",
        "minimum": 1,
        "maximum": 60
      },
      "compare": {
        "title": "Compare with an expense ratio of",
        "description": "The expense ratio of another fund, for example an actively managed fund, to compare with.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 5
      }
    }
  },
  "outputs": {
    "value": {
      "label": "Index fund value",
      "description": "The value at the end, after the expense ratio.",
      "format": "money"
    },
    "paidIn": {
      "label": "Money put in",
      "description": "The initial investment plus every addition.",
      "format": "money"
    },
    "growth": {
      "label": "Growth",
      "description": "The value minus the money put in.",
      "format": "money"
    },
    "expenses": {
      "label": "Expenses paid",
      "description": "All the monthly expenses of the index fund added up.",
      "format": "money"
    },
    "other": {
      "label": "Value in the higher-fee fund",
      "description": "The same money at the same return after the comparison expense ratio.",
      "format": "money"
    },
    "kept": {
      "label": "Kept by the lower fee",
      "description": "The index fund’s value minus the higher-fee fund’s value.",
      "format": "money"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "initial": 10000,
      "monthly": 500,
      "ret": 7,
      "er": 0.05,
      "years": 30,
      "compare": 1
    },
    "outputs": {
      "value": 653984.1709025052,
      "paidIn": 190000,
      "growth": 463984.17090250517,
      "expenses": 3464.209065949515,
      "other": 537957.2866073863,
      "kept": 116026.88429511886
    },
    "text": "$10,000.00 plus $500.00 a month at 7% a year, with a 0.05% expense ratio, grows to $653,984.17 in 30 years."
  },
  "examples": [
    {
      "given": {
        "initial": 100000,
        "monthly": 0,
        "ret": 4,
        "er": 0.25,
        "compare": 1,
        "years": 20
      },
      "expect": {
        "value": 208424.9949353171,
        "other": 179379.0329121607,
        "kept": 29045.962023156404
      },
      "source": "SEC Investor Bulletin, How Fees and Expenses Affect Your Investment Portfolio: about $208,000 with a 0.25% fee and $179,000 with 1% after 20 years (https://www.investor.gov/sites/default/files/ib_fees_expenses.pdf); Python 3 cross-check"
    },
    {
      "given": {
        "initial": 0,
        "monthly": 500,
        "ret": 7,
        "er": 0,
        "years": 30
      },
      "expect": {
        "value": 584726.3016433007,
        "paidIn": 180000
      },
      "source": "future value of monthly additions at the monthly rate (1 + R)^(1/12) − 1 (Microsoft Excel FV function, https://support.microsoft.com/en-us/office/fv-function-2eef9f44-a084-4c61-bdd8-4fe4bb1b71b3); Python 3 cross-check"
    },
    {
      "given": {
        "initial": 10000,
        "monthly": 500,
        "ret": 7,
        "er": 0.05,
        "compare": 1,
        "years": 30
      },
      "expect": {
        "value": 653984.1709025053,
        "other": 537957.2866073839,
        "expenses": 3464.2090659495148
      },
      "source": "SEC Investor Bulletin, How Fees and Expenses Affect Your Investment Portfolio: an ongoing fee reduces the value (https://www.investor.gov/sites/default/files/ib_fees_expenses.pdf); Python 3 cross-check"
    }
  ],
  "sources": [
    "U.S. Securities and Exchange Commission, Investor.gov: Index Funds. https://www.investor.gov/introduction-investing/investing-basics/investment-products/mutual-funds-and-exchange-traded-4",
    "U.S. Securities and Exchange Commission, Investor Bulletin: How Fees and Expenses Affect Your Investment Portfolio. https://www.investor.gov/sites/default/files/ib_fees_expenses.pdf",
    "U.S. Securities and Exchange Commission, Investor.gov: Understanding Fees. https://www.investor.gov/introduction-investing/getting-started/understanding-fees"
  ],
  "related": [
    "mutual-fund",
    "investment",
    "compound-interest",
    "rate-of-return",
    "cagr"
  ],
  "changelog": []
}