{
  "id": "annuity",
  "version": "6fed2065af90",
  "status": "published",
  "name": "Annuity Calculator",
  "question": "How will my annuity grow?",
  "summary": "Computes the value of a fixed deferred annuity from a premium, yearly additions, and a fixed rate, its value after tax, and the same money in a taxable account.",
  "category": "finance",
  "subcategory": "retirement",
  "url": "https://www.acalculator.org/finance/annuity-calculator",
  "markdown": "https://www.acalculator.org/finance/annuity-calculator.md",
  "kind": "schedule",
  "method": "Each year, value = (value + addition) × (1 + r); after tax = value − tax × (value − money put in); a taxable account grows by (1 + r × (1 − tax)) each year.",
  "assumptions": [
    "The rate stays the same every year, as in a fixed or multi-year guaranteed annuity.",
    "Additions are made at the start of each year, including the first.",
    "Interest is credited once a year at the yearly rate.",
    "Surrender charges, fees, and riders are not included. Taking money out early can cost surrender charges.",
    "“After tax” taxes all the interest at one rate, as if you took it all out at once, and leaves out the 10% additional tax before age 59½.",
    "This is an estimate for planning, not financial advice."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "premium": {
        "title": "Starting premium",
        "description": "The amount you put into the annuity at the start.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 1000000000
      },
      "add": {
        "title": "Added each year",
        "description": "An extra amount added at the start of every year, including the first.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 100000000
      },
      "rate": {
        "title": "Yearly interest rate",
        "description": "The yearly rate the annuity credits, as the percent the value grows in a year.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 20
      },
      "years": {
        "title": "For how long? (years)",
        "description": "How many years the annuity grows before payouts or a withdrawal.",
        "type": "integer",
        "minimum": 1,
        "maximum": 50
      },
      "tax": {
        "title": "Your tax rate",
        "description": "Your income tax rate, used on the annuity’s earnings when they come out and on a taxable account’s interest each year.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 60
      }
    }
  },
  "outputs": {
    "value": {
      "label": "Your annuity will be worth",
      "description": "The annuity value at the end of the last year, before tax.",
      "format": "money"
    },
    "paidIn": {
      "label": "Money put in",
      "description": "The premium plus every addition.",
      "format": "money"
    },
    "interest": {
      "label": "Interest earned",
      "description": "The value minus the money put in.",
      "format": "money"
    },
    "afterTax": {
      "label": "After tax, if you take it all out",
      "description": "The value minus tax at your rate on the interest earned.",
      "format": "money"
    },
    "taxable": {
      "label": "Same money in a taxable account",
      "description": "The balance if the same money earned the same rate but paid tax on the interest every year.",
      "format": "money"
    },
    "deferral": {
      "label": "Gain from tax deferral",
      "description": "The annuity after tax minus the taxable account.",
      "format": "money"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "premium": 100000,
      "add": 0,
      "rate": 5,
      "years": 10,
      "tax": 24
    },
    "outputs": {
      "value": 162889.46267774416,
      "paidIn": 100000,
      "interest": 62889.46267774416,
      "afterTax": 147795.99163508555,
      "taxable": 145202.3132046156,
      "deferral": 2593.6784304699395
    },
    "text": "At 5% a year, an annuity with $100,000.00 put in grows to $162,889.46 in 10 years, or $147,795.99 after tax if you take it all out."
  },
  "examples": [
    {
      "given": {
        "premium": 100000,
        "rate": 5,
        "years": 10,
        "tax": 24
      },
      "expect": {
        "value": 162889.4626777442,
        "interest": 62889.46267774419,
        "afterTax": 147795.99163508558,
        "taxable": 145202.3132046156,
        "deferral": 2593.6784304699686
      },
      "source": "hand calculation in content.mdx: 100,000 × 1.05^10; 100,000 × 1.038^10"
    },
    {
      "given": {
        "premium": 10000,
        "add": 5000,
        "rate": 4,
        "years": 3,
        "tax": 0
      },
      "expect": {
        "value": 27480.960000000003,
        "paidIn": 25000,
        "deferral": 0
      },
      "source": "hand calculation in content.mdx: 15,000 × 1.04³ + 5,000 × (1.04² + 1.04)"
    },
    {
      "given": {
        "premium": 50000,
        "rate": 0,
        "years": 5,
        "tax": 30
      },
      "expect": {
        "value": 50000,
        "interest": 0,
        "afterTax": 50000
      },
      "source": "hand calculation in content.mdx: no interest at 0%"
    }
  ],
  "sources": [
    "U.S. Securities and Exchange Commission, Investor.gov: Annuities (fixed, indexed, and variable annuities; surrender charges; taxes; claims-paying ability). https://www.investor.gov/introduction-investing/investing-basics/investment-products/insurance-products/annuities",
    "Internal Revenue Service, Publication 575, Pension and Annuity Income. https://www.irs.gov/publications/p575",
    "Accumulation of level deposits: S. A. Broverman, Mathematics of Investment and Credit, chapter 2."
  ],
  "related": [
    "annuity-payout",
    "future-value"
  ],
  "changelog": []
}