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Accumulation · regular contributions
Compound growth with monthly contributions
Project a balance from a starting amount, a monthly contribution, an annual rate and a time horizon, split into what you put in and what growth added.
Verified engine
What the engine returns
Read the three outputs together rather than the balance alone. Total contributed is what you chose to put in; total growth is what the horizon and the rate did with it; the future value is their sum and is the least informative of the three on its own.
Inputs the result is built from
Starting principal
Monthly contribution
Annual rate of return
Time horizon
How the result is derived
MethodFuture value of a lump sum plus the future value of a level ordinary annuity, over monthly periods derived from the annual rate and the horizon.
StandardStandard compound-interest and ordinary-annuity accumulation relations
GuardThe horizon must be greater than zero — there is no accumulation over no time.
How the money pulls ahead of what was put in
Why the split between contributions and growth is the whole point
Two engines drive the balance and they behave nothing alike. The starting amount compounds for the whole horizon; each monthly contribution compounds only for the time remaining after it arrives. The last contribution earns almost nothing, and the first earns almost everything a contribution can.
That is why the split matters. Total contributed is a decision about your budget and it is linear — double the monthly amount and it doubles. Total growth is a decision about time and rate, and it is not linear in either. Looking only at the ending balance makes both look like the same lever, and they are not.
The rate is annual and the contributions are monthly, so the two have to be reconciled before anything can be added up. The convention here divides the annual rate into monthly periods rather than compounding an effective annual rate downward. Which convention is used changes the answer, so it is stated rather than assumed.
Nothing here is a forecast. A constant rate is an arithmetic assumption, not a claim about any market: real returns arrive unevenly and the order they arrive in changes the outcome even when the average is identical. This answers what a steady rate would produce, which is a useful baseline and not a prediction.
Future value of a lump sum plus the future value of a level ordinary annuity, over monthly periods derived from the annual rate and the horizon.
When this calculation is used
- Seeing what a regular monthly contribution becomes over a long horizon, and how much of that is growth rather than deposits.
- Testing whether starting earlier or contributing more does more for the same total outlay.
- Sanity-checking a projection quoted elsewhere against the assumptions it was built on.
- Setting a realistic horizon by seeing how late the growth actually arrives.
Worked example
Take a modest starting balance, a monthly contribution you could actually sustain, an ordinary long-run rate and a horizon of several years.
Read the three outputs together rather than the balance alone. Total contributed is what you chose to put in; total growth is what the horizon and the rate did with it; the future value is their sum and is the least informative of the three on its own.
Now double the horizon without changing anything else. Total contributed merely doubles, because it is linear in time. Total growth does considerably more than double. That gap is the entire argument for starting earlier rather than contributing harder later.
What each input represents
Starting principal
What is in the account before any contribution is made. It compounds for the entire horizon, which is why it carries more weight than its size suggests. Zero is allowed if you are starting from nothing.
Monthly contribution
The amount added at each monthly period. It is treated as constant for the whole horizon; if your real contribution will rise, this understates the result, and running it again at the higher amount brackets the answer rather than averaging it.
Annual rate of return
The nominal annual rate as a percentage, before inflation, tax and fees. It is divided into monthly periods. This is a growth rate you supply, not one the calculator knows — a fund quote is not the same as a realised return.
Time horizon
How long the money stays invested. This is the input the growth figure is most sensitive to, and the one people most often shorten in a projection to make it feel realistic.
Assumptions and limits
- The rate is constant for the whole horizon and applied to every period equally.
- Contributions are the same each month and arrive at the end of their period.
- The annual rate is divided into monthly periods — a nominal convention, not an effective annual rate compounded down.
- Returns are before inflation, tax and fees, so the figure is nominal rather than spendable.
- No contribution is missed, withdrawn or increased part-way through.
What the guards protect against
- The horizon must be greater than zero — there is no accumulation over no time.
- The rate is bounded to a realistic range; a value outside it is refused rather than answered, because the result would not describe any account.
- Negative contributions are refused. A regular withdrawal is a drawdown problem with different arithmetic, not a contribution with a minus sign.
Provenance
Standard compound-interest and ordinary-annuity accumulation relations
Future value of a lump sum plus the future value of a level ordinary annuity, over monthly periods derived from the annual rate and the horizon.
Educational reference, not investment advice and not a forecast. The signed pack carries its own citation; the page reports the verification state of the release it mounted rather than asserting one.