{
  "id": "compound-interest",
  "version": "31dd1260cad8",
  "status": "published",
  "name": "Compound Interest Calculator",
  "question": "What will compound interest earn?",
  "summary": "Computes the balance of savings that earn compound interest, with optional monthly top-ups, and how much of it is interest.",
  "category": "finance",
  "subcategory": "investing",
  "url": "https://www.acalculator.org/finance/compound-interest-calculator",
  "markdown": "https://www.acalculator.org/finance/compound-interest-calculator.md",
  "kind": "schedule",
  "method": "Each month, add interest at the monthly rate (1 + r/m)^(m/12) − 1, where r is the yearly rate and m the compounding times a year, then add the top-up.",
  "assumptions": [
    "The rate does not change.",
    "Top-ups are added at the end of each month; a yearly top-up is split into 12 equal monthly ones.",
    "With quarterly or yearly compounding, interest builds at the equivalent monthly rate, so the balance matches A = P(1 + r/m)^(mt) at every compounding date.",
    "Tax and fees are not included.",
    "“In today’s money” divides the final balance by (1 + inflation)^years."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "principal": {
        "title": "Starting amount",
        "description": "The amount saved today, at the start.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 1000000000
      },
      "add": {
        "title": "Regular top-up",
        "description": "A top-up added at the end of every month. A yearly amount is split into 12 equal monthly top-ups.",
        "type": "number",
        "x-unit": "USD",
        "x-period": "month",
        "minimum": 0,
        "maximum": 100000000
      },
      "rate": {
        "title": "Interest rate",
        "description": "The nominal yearly interest rate.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 100
      },
      "years": {
        "title": "For how long? (years)",
        "description": "How many years the money grows.",
        "type": "integer",
        "minimum": 1,
        "maximum": 60
      },
      "comp": {
        "title": "How often is interest added?",
        "description": "How many times a year interest is added to the balance: monthly (12), quarterly (4), or yearly (1).",
        "type": "string",
        "enum": [
          "12",
          "4",
          "1"
        ]
      },
      "start": {
        "title": "Start date",
        "description": "The day the savings start. It labels the months and gives the end date.",
        "type": "string",
        "format": "date"
      },
      "inflation": {
        "title": "Prices rise each year by",
        "description": "The yearly inflation rate used to show the balance in today’s money.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 50
      }
    }
  },
  "outputs": {
    "fv": {
      "label": "You’ll have",
      "description": "The balance at the end of the last month.",
      "format": "money"
    },
    "plan": {
      "label": "Your savings plan",
      "description": "The starting amount, the monthly top-up, and the number of years, in words.",
      "format": "text"
    },
    "paidIn": {
      "label": "Your money",
      "description": "The starting amount plus every top-up.",
      "format": "money"
    },
    "interest": {
      "label": "Interest",
      "description": "All the interest earned: the final balance minus your money.",
      "format": "money"
    },
    "lastYear": {
      "label": "Interest in the last year",
      "description": "The interest earned in the final 12 months.",
      "format": "money"
    },
    "doubling": {
      "label": "Years to double your money",
      "description": "How many years a balance takes to double at this rate with no top-ups: ln 2 ÷ ln(1 + yearly effective rate).",
      "format": "number"
    },
    "real": {
      "label": "In today’s money",
      "description": "The final balance divided by (1 + inflation) to the power of the years.",
      "format": "money"
    },
    "end": {
      "label": "Ends in",
      "description": "The month of the final balance, when a start date is given.",
      "format": "month-year"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "principal": 10000,
      "add": 0,
      "rate": 5,
      "years": 10,
      "comp": "12",
      "start": "2026-10-05",
      "inflation": 3
    },
    "outputs": {
      "fv": 16470.094976902827,
      "plan": "$10,000.00 now for 10 years",
      "paidIn": 10000,
      "interest": 6470.094976902827,
      "lastYear": 801.6284827378278,
      "doubling": 13.891804729054316,
      "real": 12255.297450084508,
      "end": "2036-10-05"
    },
    "text": "$10,000.00 now for 10 years at 5% a year grows to $16,470.09, of which $6,470.09 is interest."
  },
  "examples": [
    {
      "given": {
        "principal": 10000,
        "rate": 5,
        "years": 10,
        "comp": "12"
      },
      "expect": {
        "fv": 16470.0949769028,
        "interest": 6470.0949769028
      },
      "source": "SEC Investor.gov formula A = P(1 + r/n)^(nt); hand calculation in content.mdx"
    },
    {
      "given": {
        "principal": 1000,
        "rate": 5,
        "years": 10,
        "comp": "1"
      },
      "expect": {
        "fv": 1628.894626777442
      },
      "source": "the old page FAQ; hand calculation in content.mdx"
    },
    {
      "given": {
        "principal": 0,
        "add": 100,
        "rate": 6,
        "years": 10,
        "comp": "12"
      },
      "expect": {
        "fv": 16387.9346806458,
        "paidIn": 12000
      },
      "source": "future value of an annuity; hand calculation in content.mdx"
    },
    {
      "given": {
        "principal": 10000,
        "rate": 6,
        "years": 5,
        "comp": "1",
        "start": "2026-10-01"
      },
      "expect": {
        "fv": 13382.255776,
        "doubling": 11.895661045941875,
        "end": "2031-10-01"
      },
      "source": "hand calculation in content.mdx"
    }
  ],
  "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 and effective annual rate: S. A. Broverman, Mathematics of Investment and Credit, chapters 1 and 2."
  ],
  "related": [
    "savings",
    "investment",
    "apy",
    "cd",
    "simple-interest"
  ],
  "changelog": [
    {
      "date": "2026-09-29",
      "note": "The top-up box is labelled Regular top-up, since it takes a monthly or a yearly amount; related links go to savings pages (user test 2026-09-29)."
    },
    {
      "date": "2026-10-01",
      "note": "The answer sentence names the monthly top-ups and says “1 year”, not “1 years”."
    }
  ]
}