{
    "name": "Annuity Calculator",
    "url": "https://calculators.geekmidst.com/calculators/annuity-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/annuity-calculator.md",
    "category": "Finance",
    "description": "Find the future value and present value of a series of equal payments, paid at the start or end of each period, with an optional starting balance.",
    "summary": "An annuity is a series of equal payments at regular intervals. Its future value is what the payments grow to; its present value is what they are worth today.",
    "also_called": [
        "Future value of annuity calculator",
        "Present value of annuity calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "payment",
            "label": "Payment per period",
            "type": "number",
            "default": "500"
        },
        {
            "name": "frequency",
            "label": "Payments per year",
            "type": "select",
            "default": "12",
            "options": {
                "1": "Yearly",
                "2": "Half-yearly",
                "4": "Quarterly",
                "12": "Monthly"
            }
        },
        {
            "name": "rate",
            "label": "Interest rate (per year)",
            "type": "number",
            "default": "5",
            "unit": "%"
        },
        {
            "name": "years",
            "label": "Years",
            "type": "number",
            "default": "20"
        },
        {
            "name": "timing",
            "label": "Payments made at",
            "type": "segmented",
            "default": "end",
            "options": {
                "end": "End of period",
                "begin": "Start of period"
            }
        },
        {
            "name": "principal",
            "label": "Starting balance",
            "type": "number",
            "default": "0",
            "optional": true
        },
        {
            "name": "currency",
            "label": "Currency",
            "type": "currency",
            "default": "USD"
        }
    ],
    "outputs": [
        {
            "key": "fv",
            "label": "Future value",
            "format": "currency"
        },
        {
            "key": "pv",
            "label": "Present value (incl. starting balance)",
            "format": "currency"
        },
        {
            "key": "pv_payments",
            "label": "Present value of the payments",
            "format": "currency"
        },
        {
            "key": "total_payments",
            "label": "Total payments",
            "format": "currency"
        },
        {
            "key": "interest",
            "label": "Interest earned",
            "format": "currency"
        },
        {
            "key": "periods",
            "label": "Number of payments",
            "format": "integer"
        }
    ],
    "formula": {
        "text": "FV = P(1 + i)^n + PMT × ((1 + i)^n − 1) ÷ i × (1 + i if paid at the start);  PV = PMT × (1 − (1 + i)^−n) ÷ i × (1 + i if paid at the start)",
        "variables": {
            "PMT": "payment per period",
            "i": "annual rate ÷ payments per year",
            "n": "years × payments per year",
            "P": "starting balance"
        }
    },
    "worked_example": {
        "inputs": {
            "payment": "1000",
            "frequency": "1",
            "rate": "5",
            "years": "10",
            "timing": "end",
            "principal": "0",
            "currency": "USD"
        },
        "steps": [
            "i = 5% ÷ 1 = 0.05; n = 10.",
            "FV = 1,000 × (1.05^10 − 1) ÷ 0.05 = 1,000 × 12.5779 = 12,577.89.",
            "PV = 1,000 × (1 − 1.05^−10) ÷ 0.05 = 1,000 × 7.7217 = 7,721.73."
        ],
        "result": "Ten yearly payments of $1,000 at 5% grow to $12,577.89; the same payments are worth $7,721.73 today."
    },
    "interpretation": "Use the future value for saving towards a goal and the present value to price a stream of payments, such as a structured settlement or a lease. Payments at the start of each period (an annuity due) earn one extra period of interest, so both values are higher by a factor of (1 + i).",
    "assumptions": [
        "The rate is constant and compounds once per payment period.",
        "All payments are the same size."
    ],
    "limitations": [
        "Insurance-company annuity products have fees, surrender charges and guarantees that this calculation does not include.",
        "Taxes and inflation are not deducted."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "What is the difference between an ordinary annuity and an annuity due?",
            "answer": "An ordinary annuity pays at the end of each period (loan repayments, most bonds). An annuity due pays at the start (rent, insurance premiums). An annuity due is worth (1 + i) times more."
        },
        {
            "question": "Is this the same as an annuity I buy from an insurer?",
            "answer": "The maths is the same, but a commercial annuity’s payout also depends on life expectancy, fees and the insurer’s pricing. Use the Annuity Payout Calculator to see what a balance can pay out."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Annuity Payout Calculator",
            "url": "https://calculators.geekmidst.com/calculators/annuity-payout-calculator"
        },
        {
            "name": "Compound Interest Calculator",
            "url": "https://calculators.geekmidst.com/calculators/compound-interest-calculator"
        },
        {
            "name": "SIP Calculator",
            "url": "https://calculators.geekmidst.com/calculators/sip-calculator"
        },
        {
            "name": "Pension Calculator",
            "url": "https://calculators.geekmidst.com/calculators/pension-calculator"
        }
    ],
    "disclaimer": "Returns are illustrations at a constant rate, not predictions or guarantees. Investments can lose value. This is not investment advice.",
    "publisher": "GM¹X CalcVerse"
}