A folio of household instruments · Independent publication

Lake Oswego Finance Almanac Mortgage · Growth · Net Worth

Instrument the second

Compound Growth Illustration

Begin with a sum, add a fixed amount each month, choose a yearly rate and a horizon. The page draws what you put in and what the arithmetic adds, year by year.

The assumptions

These starting values are illustrations. The rate is a number you choose, not a prediction, a quotation or a description of any real account. Contributions are assumed to arrive at the end of each month and growth is compounded monthly.

Total contributed

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starting sum plus every monthly addition

Illustrated balance at the horizon

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Growth added by the arithmetic

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Contributions and growth, drawn apart

The shaded lower region is money you put in; the region above it, up to the solid line, is growth. The dotted lines mark the same plan at two points lower and two points higher, to show how much the rate assumption matters. None of them is a prediction.

    The same plan at three rates

    A lower or higher assumed rate changes only the growth column. The money you contribute is identical in every row.

    A reading aid

    Dividing 72 by a yearly rate gives a rough number of years for a sum to double, with nothing added. It is a rule of thumb, not a result, and it works best for rates in the middle of the range.

    Enter a rate above zero to see the rule applied.

    The ledger, year by year

    Balances are shown at the end of each year.

    Reading notes

    What this page does, and what it does not

    How to use it

    1. Enter a starting sum, which may be zero if you are beginning from nothing.
    2. Enter the amount you intend to add each month, which may also be zero.
    3. Choose a yearly rate. Try several, including a low one; a plan that only works at a high rate deserves scrutiny.
    4. Choose a horizon in whole years, from 1 to 60, and read the balance and the split between contributions and growth.
    5. Use the slider to find the month in which growth first exceeds the money you have put in, if it does.

    What it assumes

    • One constant yearly rate, applied as one twelfth each month. Real accounts rise and fall, and a constant rate hides that entirely.
    • Contributions land at the end of every month and never stop. No withdrawals, fees, taxes or inflation are modelled.
    • Amounts are in nominal dollars. A sum far in the future will buy less than the same number does today, by an amount this page does not estimate.

    Edge cases

    • A rate of zero is allowed and simply adds up your contributions. A negative rate down to minus ten is allowed, to show what steady losses would do.
    • The band uses the rate minus two points and plus two points, and may therefore dip below zero for low rates.
    • Blank, non-numeric or absurdly large entries produce a plain message in place of a result.

    A word of caution

    The balance at the horizon is the output of a formula, not a promise from any institution. Nobody can guarantee a rate over decades. Use this page to understand how time, saving and rate interact, and take decisions to a qualified professional who knows your situation.