{
  "id": "future-value",
  "version": "57aae22dc8c2",
  "status": "published",
  "name": "Future Value Calculator",
  "question": "What is the future value?",
  "summary": "Computes the future value of a present amount plus a level payment each period, at a yearly rate compounded 1, 2, 4, or 12 times a year, with payments at the start or end of each period.",
  "category": "finance",
  "subcategory": "investing",
  "url": "https://www.acalculator.org/finance/future-value-calculator",
  "markdown": "https://www.acalculator.org/finance/future-value-calculator.md",
  "kind": "schedule",
  "method": "FV = PV × (1 + r)^n + PMT × ((1 + r)^n − 1) ÷ r, times (1 + r) on the payments when they are made at the start of each period, with r = yearly rate ÷ periods a year and n = years × periods a year; worked period by period.",
  "assumptions": [
    "The rate stays the same for every period, and interest is added once per period.",
    "All payments are the same size, one per period.",
    "No fees or taxes are taken out.",
    "This is an estimate for planning, not financial advice."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "pv": {
        "title": "Starting amount (present value)",
        "description": "The amount you have at the start, before the first period.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 1000000000
      },
      "pmt": {
        "title": "Payment each period",
        "description": "The amount added every period (the annuity payment). Leave it empty or 0 for a single sum.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 100000000
      },
      "rate": {
        "title": "Yearly interest rate",
        "description": "The nominal yearly rate. The rate per period is this divided by the periods a year.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 100
      },
      "freq": {
        "title": "Periods a year",
        "description": "How many times a year interest is added and a payment is made: yearly (1), twice a year (2), quarterly (4), or monthly (12).",
        "type": "string",
        "enum": [
          "1",
          "2",
          "4",
          "12"
        ]
      },
      "years": {
        "title": "Number of years",
        "description": "How many years the money grows. The number of periods is years × periods a year.",
        "type": "integer",
        "minimum": 1,
        "maximum": 100
      },
      "when": {
        "title": "Payments are made at the",
        "description": "End of each period (an ordinary annuity) or the start of each period (an annuity due). A payment at the start earns one more period of interest.",
        "type": "string",
        "enum": [
          "end",
          "start"
        ]
      }
    }
  },
  "outputs": {
    "fv": {
      "label": "Future value",
      "description": "The balance at the end of the last period.",
      "format": "money"
    },
    "paidIn": {
      "label": "Money put in",
      "description": "The starting amount plus every payment.",
      "format": "money"
    },
    "interest": {
      "label": "Interest",
      "description": "All the interest earned: the future value minus the money put in.",
      "format": "money"
    },
    "fvPv": {
      "label": "Future value of the starting amount",
      "description": "What the starting amount alone grows to: PV × (1 + r)^n.",
      "format": "money"
    },
    "fvPmt": {
      "label": "Future value of the payments",
      "description": "What the payments alone grow to: PMT × ((1 + r)^n − 1) ÷ r, times (1 + r) at the start; 0 with no payment.",
      "format": "money"
    },
    "periods": {
      "label": "Number of periods",
      "description": "Years × periods a year.",
      "format": "integer"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "pv": 10000,
      "pmt": 100,
      "rate": 6,
      "freq": "1",
      "years": 10,
      "when": "end"
    },
    "outputs": {
      "fv": 19226.55645966663,
      "paidIn": 11000,
      "interest": 8226.55645966663,
      "fvPv": 17908.476965428534,
      "fvPmt": 1318.0794942380892,
      "periods": 10
    },
    "text": "At 6% a year for 10 years, $11,000.00 put in grows to a future value of $19,226.56."
  },
  "examples": [
    {
      "given": {
        "pv": 1000,
        "rate": 5,
        "freq": "1",
        "years": 10,
        "when": "end"
      },
      "expect": {
        "fv": 1628.894626777442,
        "interest": 628.894626777442,
        "fvPv": 1628.894626777442
      },
      "source": "FV = PV × (1 + r)^n, hand calculation in content.mdx"
    },
    {
      "given": {
        "pv": 0,
        "pmt": 100,
        "rate": 6,
        "freq": "1",
        "years": 10,
        "when": "end"
      },
      "expect": {
        "fv": 1318.079494238091,
        "paidIn": 1000,
        "fvPv": 0,
        "fvPmt": 1318.079494238091
      },
      "source": "future value of an ordinary annuity, PMT × ((1 + r)^n − 1) ÷ r; hand calculation in content.mdx"
    },
    {
      "given": {
        "pv": 0,
        "pmt": 100,
        "rate": 6,
        "freq": "1",
        "years": 10,
        "when": "start"
      },
      "expect": {
        "fv": 1397.1642638923765
      },
      "source": "future value of an annuity due, times (1 + r); hand calculation in content.mdx"
    },
    {
      "given": {
        "pv": 0,
        "pmt": 100,
        "rate": 6,
        "freq": "12",
        "years": 10,
        "when": "end"
      },
      "expect": {
        "fv": 16387.9346806458,
        "periods": 120
      },
      "source": "monthly: r = 0.5%, n = 120, 100 × (1.005^120 − 1) ÷ 0.005; hand calculation in content.mdx"
    },
    {
      "given": {
        "pv": 1000,
        "pmt": 100,
        "rate": 0,
        "freq": "1",
        "years": 12,
        "when": "end"
      },
      "expect": {
        "fv": 2200,
        "interest": 0
      },
      "source": "hand calculation in content.mdx: 1,000 + 12 × 100"
    }
  ],
  "sources": [
    "U.S. Securities and Exchange Commission, Investor.gov compound interest calculator and formula. https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator",
    "Future value of an annuity immediate and an annuity due: S. A. Broverman, Mathematics of Investment and Credit, chapter 2."
  ],
  "related": [
    "compound-interest",
    "investment",
    "annuity"
  ],
  "changelog": []
}