Compound Growth Calculator
Compound growth is growth calculated on previous growth as well as on the original amount, which is why the curve bends upward rather than running straight. Time matters more than the rate, and regular contributions change the shape of the result entirely.
What it becomes
Monthly contributions, compounded monthly. The rate is an assumption; the horizon is a decision.
The rule of 72 in the last output is an approximation, not the formula. Dividing 72 by the rate gives the doubling time to within a few months at ordinary rates, and drifts once the rate gets large.
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How the number is built
Simple growth pays a return on the original amount. Compound growth pays a return on the original amount and on every return before it, which is why the line curves rather than running straight.
With a starting sum and regular additions, the formula has two halves:
Final = start × (1 + r)^n + monthly × ((1 + r)^n − 1) ÷ r
where r is the monthly rate and n the number of months. The first term compounds what you began with; the second compounds each contribution for however long it has been invested.
A worked example
Take the defaults: 10,000 to start, 500 a month, 7% a year, for 25 years.
You contribute 10,000 + (500 × 300) = 160,000.
The final value is 462,290.
So 302,290 of it is growth — 65% of the result is money nobody contributed. That ratio is the thing worth internalizing, and it climbs the longer the horizon runs.
The rule of 72 gives a fast check. 72 ÷ 7 = 10.3 years to double. It is an approximation, close at ordinary rates and increasingly wrong as the rate rises — at 20% it says 3.6 years where the exact answer is 3.8.
Time against rate
Run the same contributions at different horizons and rates and the asymmetry is stark.
At 7% for 25 years the default gives 462,290. At 7% for 35 years it gives 1,015,589 — ten more years more than doubles it, on the same monthly amount.
At 9% for 25 years it gives 654,645. Two extra percentage points of return, sustained for a quarter century, add 192,355 — where the ten extra years added 553,299.
The rate is the thing people try to control and the horizon is the thing that actually pays. One of those is under your control and the other is a forecast.
Which is why a late start is expensive in a way extra contributions cannot fully fix. Money added in year one compounds for 25 years; money added in year 20 compounds for five.
Why the last third does the most
Split the default 25 years into three stretches and the work is wildly uneven.
After 8 years the balance is 81,578, against $58,000 contributed. Growth has added 23,578 — real, and smaller than the contributions.
After 16 years it is 206,683, against $106,000 contributed. Growth has now added 100,683 and is about to overtake what was put in, which on these defaults happens between sixteen and seventeen years in.
After 25 years it is 462,290, against $160,000 contributed. The final nine years added 255,607 — more than the first sixteen years produced in total.
That shape is why patience is the active ingredient. The curve does least when motivation is highest and most once the account has become boring, and no part of it can be brought forward.
The picture below draws the same defaults month by month. Growth first passes the money paid in at month 200, sixteen years and eight months in, and from there it pulls away.
What compounds against you
A fee runs on exactly the same curve, in the opposite direction. A basis point is one hundredth of a percent (75 basis points is 0.75%). On this site’s arithmetic, 5 basis points a year removes 1.5% of a thirty-year pot, 20 removes 5.8%, 75 removes 20.2% and 150 removes 36.5%.
And inflation compounds too. At 3% a year, the 462,290 above is worth 220,792 in present money. Both numbers are correct; only one of them buys anything.
The original data
Of the 24,971 unique videos in this site’s search study, 9 have compound or compounding in the title, at a median of 79,381 views across 9 channels, 4 of them instruction-shaped. Index funds appear in 132 at 69,951 and retirement targets in 17 at 87,636.
The question: Ten years in and it looks slow. Give up?
Nine videos at a 79,381 median. The single most important idea in long-term investing has almost no instructional coverage, because it is a formula rather than a story — which is the pattern behind every tool on this site.
The answer is that ten years in is exactly when it looks slow. On the default figures the balance after ten years is 106,639 against $70,000 contributed — the growth is real but it has not yet overtaken the contributions. The curve does most of its work in the final third, so the years that feel least rewarding are the ones that make the last third possible.
When it fails
The formula assumes a constant return, and no real return is constant. A market that averages 7% delivers it as +22%, −9%, +14%, −3% and so on, and the order matters — a bad decade at the start leaves a permanently smaller base to compound from, while the same decade at the end does far less damage. This calculator cannot see that, and it is the single largest gap between the smooth curve and a real account.
The second failure is stopping contributions during a fall. That is when contributions buy the most, and it is when people most want to stop.
A third is using a nominal return without adjusting for inflation. The final figure is future money, not present money.
A fourth is ignoring the fee. It compounds on the same curve and it is certain where the return is not.
A fifth is treating the output as a forecast. It is arithmetic on an assumption, and the assumption is the uncertain part.
And a sixth is comparing a compounded projection against an uncompounded one. Doubling the rate does not double the result, and halving the horizon does far more than halve it.
Related
Compound interest covers the mechanism and why compounding frequency matters less than people expect. Index funds is where most of this money actually sits. And dollar-cost averaging is the contribution schedule the second half of the formula assumes.
The surprising part of running this properly is how much of the final number is growth rather than money paid in. On the default figures, 160,000 goes in and 462,290 comes out — so nearly two thirds of the result was never contributed by anyone. That is the entire argument for starting early, and it is arithmetic rather than motivation.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.