Millionaire Calculator
Years to a million is the compound growth formula solved for time rather than for a balance. Contributions and the horizon both move the answer, but the horizon does more work, and a million reached decades from now buys considerably less than a million today.
How long the target takes
Defaults start from 10,000, add 800 a month, assume 8%, and aim at 1,000,000.
This is the compound growth formula solved for time, which is why a logarithm appears. The answer is what one assumed rate implies, not a date — and the assumed rate is the input least under your control.
Runs entirely in your browser. Nothing you type is sent anywhere or stored.
How the number is built
This is not a new formula. It is the compound growth equation with the balance known and the horizon unknown, which is what puts a logarithm in the answer.
Months = log((target × r + monthly) ÷ (start × r + monthly)) ÷ log(1 + r)
Every contribution starts working the month it arrives, so the schedule matters as much as the total. The same money added over ten years does far more than the same money added over three.
A worked example
Take the defaults: 10,000 to start, 800 a month, an assumed 8%, aiming at 1,000,000.
It takes 324.1 months — 27.0 years.
Over that stretch you contribute 269,286.
So 730,714 of the target is growth — 73% of it, produced by the horizon rather than the saving.
Change one input at a time and the sensitivity is clear. At 6% the answer is 32.1 years, at 8% it is 27.0, at 10% it is 23.5 and at 12% it is 20.8.
Change the contribution instead. At 500 a month it takes 31.8 years, at 800 it takes 27.0, at 1,200 it takes 22.9 and at 2,000 it takes 18.0.
Both levers work and only one is under your control. The return is a forecast you make about markets; the contribution is a decision you make about spending, and it is the one that can be acted on this month.
A million is not what it was
At 3% inflation, the million reached in 27 years buys what 450,069 buys today. The number is correct and the milestone is smaller than it sounds, because the target is a fixed nominal figure being chased across a moving price level.
Two honest ways to handle it. Raise the target so it means today’s million at the finish — about 2,221,000 on those figures — or enter a real return instead of a nominal one, roughly 5% where you would have used 8%. Do one, not both, or you will double-count inflation.
The last stretch is the fastest
Ask the calculator when it passes each milestone and the spacing is uneven in a way that surprises people. On the defaults it reaches 100,000 after 6.6 years, 250,000 after 13.1, 500,000 after 19.6, 750,000 after 23.8 and the million after 27.0.
The first quarter of the target takes 13.1 years and the last quarter takes 3.2. Nothing about the contribution changed — the balance simply became large enough that its own growth outpaces what is being added.
Which is why the discouraging part is the beginning and it cannot be skipped. The years that feel least productive are the ones building the base that the final stretch runs on, and no amount of adjustment brings that forward.
What the assumption hides
Enter the return you actually receive, not the one the market produces. A fee comes off the top:
on this site’s arithmetic, 75 basis points a year removes 20.2% of a thirty-year pot and 150 removes
36.5%, with the figures in research/series-measurements.json. An 8% assumption against a 1% fee is
really a 7% assumption.
The rate is also an average of something that never behaves like an average. On this site’s shared series, 95% of bars sit below a prior peak and the longest stretch under water ran 73 bars — and it still finished up 3.61%. The destination can be reached by a path that looks nothing like the line.
The original data
Of the 24,971 unique videos in research/search-study-corpus.jsonl, 81 have an instruction-shaped
title about reaching a million, at a median of 85,819 views across 70 channels — and 1% are
calculator-shaped. Compound growth appears in 9 at 79,381 and retirement targets in 16 at 101,960.
The counts come from site/rank_tools2.py, which deduplicates by video id.
Eighty-one videos across seventy channels, and one percent of them offer a calculator. It is the most-covered subject measured here and almost none of the coverage hands anyone the arithmetic, which is the gap this page exists to fill.
The answer to the question on that chart is that raising the assumed rate shortens the date on paper and widens the range of real outcomes. Moving from 8% to 12% saves 6.2 years in the formula and buys a path where the drawdowns are far deeper. On this site’s measured leverage series, 3x returned 8.93% against a naive 10.83% while the drawdown went from 3.76% to 11.08% — the loss scaled with the multiple and the return did not.
When it fails
A decade of flat returns simply moves the date, and the formula never tells you it has. The answer is recalculated from where you actually are, so a plan built on a 27-year projection becomes a 34-year one without any single moment where the plan was declared wrong. That drift is the normal case rather than the exception, and it is the reason the date should be revisited annually rather than treated as fixed.
The second failure is a nominal target. A million in 27 years is not a million.
A third is using a gross return. Fees and taxes come out of the rate you should enter.
A fourth is assuming contributions never stop. Most people’s do, at least once.
A fifth is treating the output as a date. It is what one assumption implies.
And a sixth is raising the assumed rate to shorten it. That changes the projection, not the portfolio.
Related
Compound interest is the same formula in its usual direction. Index funds is where most of this money sits. And inflation is why the target is worth less on arrival than it is today.
The figure that reframes this is the split at the end: 269,286 contributed against 730,714 of growth. Nearly three quarters of the target is produced by the arithmetic rather than by the saving, and all of that portion is bought with time. It is why the strongest thing anyone can do about this number is start, rather than optimise.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.