Compounding is hard to feel from a percentage. Seven per cent a year sounds modest, and for the first few years it is — which is exactly why people stop. The effect that makes it worth doing does not show up until the returns start earning returns of their own, and by then the habit either exists or it does not.
This calculator makes one thing visible: how much of the final balance you never put in. It charts what you have contributed against what the account is worth, and the gap between those two lines is the whole argument.
This is for seeing what time does to money, not for planning a specific purchase. If you have a target and a date, the savings goal calculator answers that question directly; this one is about the shape of the curve rather than hitting a number.
This calculator needs JavaScript. The arithmetic by hand: multiply your balance by one plus the monthly rate, add that month's contribution, and repeat. The rule of 72 is the shortcut worth knowing — divide 72 by your annual return and you get roughly the number of years for money to double. At 7% that is about ten years.
Why the gap matters more than the total
A final balance on its own tells you very little. Two people can arrive at the same number, one having contributed nearly all of it and the other having contributed a third, and those are completely different outcomes — the second one bought the difference with time rather than with money.
That is what the chart is for. The lower line is what left your account. The upper line is what the account is worth. Early on they sit almost on top of each other, which is the part that feels like nothing is happening. The distance between them at the right-hand edge is the return doing the work you did not have to.
A worked example
$10,000 to start, $500 a month added, 7% a year, compounded monthly, left for twenty years:
The balance reaches $300,851. Of that, $130,000 is money that came out of your account — the opening $10,000 plus 240 monthly deposits. The remaining $170,851 was never contributed by you at all. It is 57% of the final balance.
The crossover — the month where growth overtakes what you have put in — lands at month 200, a little under seventeen years in. That is the number worth sitting with. For sixteen years this looks like a savings account with a good rate, and the entire argument for compounding is about what happens after that.
The crossover
Somewhere in a long enough projection there is a year where the growth becomes larger than everything you have paid in. Past that point most of the balance is money you never earned at a job, and each further year adds more than the last.
Where it lands depends far more on the length of the term than on the return. That is the uncomfortable part of compounding: it rewards having started, and there is no way to buy the missing years back later. If the crossover does not appear inside your term at all, the calculator says so rather than hiding it — at a low rate over a short period it genuinely does not happen.
What this does not include
Two things, and both make the real answer smaller.
Tax. Where you hold an investment can change the outcome by years. The projection here is gross.
Fees. A percentage charged annually compounds against you in exactly the way the return compounds for you. A 1% fee is not 1% of your money — it is a share of the growth line, taken every year, including from the growth it has already taken. Over a long term that is not a rounding error.
The return itself is the biggest assumption of all. A flat annual figure is a convenience, not a forecast; real markets deliver the same average through a completely different sequence, and the order matters as much as the average once you start withdrawing.
If you want to point this arithmetic at a specific date rather than a balance, the FIRE calculator runs it towards the year work becomes optional, and the savings goal calculator runs it backwards from a target. Our wealth guides cover the rest.