{
  "id": "annuity-payout",
  "version": "68ce92203504",
  "status": "published",
  "name": "Annuity Payout Calculator",
  "question": "What will my annuity payout be?",
  "summary": "Computes the level payout a balance can pay for a number of years while it keeps earning interest, or how long a chosen payout lasts.",
  "category": "finance",
  "subcategory": "retirement",
  "url": "https://www.acalculator.org/finance/annuity-payout-calculator",
  "markdown": "https://www.acalculator.org/finance/annuity-payout-calculator.md",
  "kind": "schedule",
  "method": "payout = P × r ÷ (1 − (1 + r)^−n), divided by (1 + r) when payouts are at the start, with r = yearly rate ÷ payouts a year; for a chosen payout, n = −ln(1 − P × r ÷ payout) ÷ ln(1 + r).",
  "assumptions": [
    "The balance earns the same rate for the whole time, at the yearly rate divided by the payouts a year.",
    "All payouts are the same size, except a smaller last one when the balance runs out part way.",
    "Fees, taxes, and surrender charges are not included.",
    "This is not a lifetime annuity quote: insurers price those with life expectancy tables and their own rates.",
    "This is an estimate for planning, not financial advice."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "principal": {
        "title": "Starting balance",
        "description": "The amount the payouts come from, for example the value of an annuity or savings.",
        "type": "number",
        "x-unit": "USD",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "rate": {
        "title": "Yearly interest rate",
        "description": "The yearly rate the balance earns. The rate per payout is this divided by the payouts a year.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 20
      },
      "find": {
        "title": "What do you want to find?",
        "description": "The payout for a number of years, or how long a payout you choose lasts.",
        "type": "string",
        "enum": [
          "amount",
          "length"
        ]
      },
      "years": {
        "title": "Pay out for (years)",
        "description": "How many years the payouts last.",
        "type": "integer",
        "minimum": 1,
        "maximum": 60
      },
      "payout": {
        "title": "Each payout",
        "description": "The amount of each payout.",
        "type": "number",
        "x-unit": "USD",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "freq": {
        "title": "How often?",
        "description": "How many payouts a year: monthly (12), quarterly (4), or yearly (1).",
        "type": "string",
        "enum": [
          "12",
          "4",
          "1"
        ]
      },
      "when": {
        "title": "Payouts are made at the",
        "description": "End of each period, so the first payout is one period from now, or the start, so the first payout is now.",
        "type": "string",
        "enum": [
          "end",
          "start"
        ]
      }
    }
  },
  "outputs": {
    "payment": {
      "label": "Each payout",
      "description": "The level payout that uses up the balance over the years you chose.",
      "format": "money"
    },
    "lasts": {
      "label": "The money lasts",
      "description": "How many years of payouts: the number of payouts divided by the payouts a year.",
      "format": "number"
    },
    "payouts": {
      "label": "Number of payouts",
      "description": "How many payouts are made, including a smaller last one.",
      "format": "integer"
    },
    "total": {
      "label": "Total paid out",
      "description": "Every payout added up.",
      "format": "money"
    },
    "interest": {
      "label": "Interest earned",
      "description": "The total paid out minus the starting balance.",
      "format": "money"
    },
    "last": {
      "label": "Last payout",
      "description": "The final payout, which is smaller when the balance runs out part way.",
      "format": "money"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "principal": 250000,
      "rate": 5,
      "find": "amount",
      "years": 20,
      "payout": 1500,
      "freq": "12",
      "when": "end"
    },
    "outputs": {
      "payment": 1649.8893480416432,
      "lasts": 20,
      "payouts": 240,
      "total": 395973.44352999184,
      "interest": 145973.44352999184
    },
    "text": "$250,000.00 earning 5% a year pays out $395,973.44 in 240 payouts over 20 years."
  },
  "examples": [
    {
      "given": {
        "principal": 250000,
        "rate": 5,
        "find": "amount",
        "years": 20,
        "freq": "12",
        "when": "end"
      },
      "expect": {
        "payment": 1649.8893480416468,
        "payouts": 240,
        "total": 395973.4435299952
      },
      "source": "level payout formula, hand calculation in content.mdx"
    },
    {
      "given": {
        "principal": 100000,
        "rate": 6,
        "find": "amount",
        "years": 10,
        "freq": "1",
        "when": "start"
      },
      "expect": {
        "payment": 12817.73190758337
      },
      "source": "annuity due: P × r ÷ ((1 − (1 + r)^−n) × (1 + r)); hand calculation in content.mdx"
    },
    {
      "given": {
        "principal": 100000,
        "rate": 0,
        "find": "length",
        "payout": 1500,
        "freq": "12",
        "when": "end"
      },
      "expect": {
        "payouts": 67,
        "lasts": 5.583333333333333,
        "last": 1000,
        "total": 100000
      },
      "source": "hand calculation in content.mdx: 66 payouts of $1,500 and a last one of $1,000"
    },
    {
      "given": {
        "principal": 200000,
        "rate": 4,
        "find": "length",
        "payout": 2000,
        "freq": "12",
        "when": "end"
      },
      "expect": {
        "payouts": 122
      },
      "source": "n = −ln(1 − P × r ÷ payout) ÷ ln(1 + r) = 121.84, so 122 payouts; hand calculation in content.mdx"
    }
  ],
  "sources": [
    "U.S. Securities and Exchange Commission, Investor.gov: Annuities. https://www.investor.gov/introduction-investing/investing-basics/investment-products/insurance-products/annuities",
    "Present value of an annuity immediate and an annuity due: S. A. Broverman, Mathematics of Investment and Credit, chapter 2."
  ],
  "related": [
    "annuity",
    "retirement-withdrawal"
  ],
  "changelog": []
}