Simple growth adds the same amount every year. Compound growth adds a percentage of a growing total — so each year's gains become next year's principal. The difference is invisible for five years and overwhelming at thirty. That's the whole trick, and it's the entire engine behind every long-term fortune on our trillionaire watchlist.
The formula: future value = P(1+r)n + C × (((1+r)n − 1) ÷ r), where P is the starting amount, r the annual rate, C the yearly contribution, and n the years.
$10,000 at 7% for 30 years, no contributions: about $76,123. The $10,000 did all the work; growth multiplied it 7.6×.
$10,000 at 7% for 30 years, plus $5,000/year: about $548,000 total — $160,000 of contributions and roughly $388,000 of growth. The contributions matter, but compounding contributed more than twice what you put in.
Rate sensitivity: the same $5,000/year for 30 years at 5% reaches about $348,000; at 9%, about $726,000. Small rate differences, enormous outcome differences — which is exactly why the assumed rate is the most dangerous number in personal finance.
Each year's growth is calculated on the previous total — including past growth. $10,000 at 7% becomes $10,700 after year one, and year two's 7% applies to $10,700. Over decades, growth-on-growth dominates.
Future value = starting amount × (1 + rate)years, plus yearly contributions × (((1 + rate)years − 1) ÷ rate). The calculator above applies it for you.
The math can show large numbers over long periods — but it assumes a constant rate, ignores inflation, fees, and taxes, and predicts nothing. Treat it as an illustration of how compounding behaves, not a plan.
Each year: balance = (balance + contribution) × (1 + rate). That's it — one line, repeated. The magic is all in the repetition: at 10% a year, money doubles roughly every 7.2 years (the rule of 72). Ten doublings is a thousand-fold gain; twenty doublings is a million-fold.
This calculator uses nominal returns (before inflation) and annual compounding for clarity. Real portfolios compound continuously and chaotically; taxes, fees, and inflation all drag. A realistic long-run stock return is often quoted around 7% real (after inflation) — noticeably slower than the 10% nominal examples above.
Early years feel pointless: $10,000 at 10% gains $1,000 in year one. But the gains themselves start gaining. By year 30 the same $10,000 seed has spawned hundreds of thousands in compounding returns. The lesson isn't "start rich" — it's "start early." A dollar invested at 25 is worth roughly ten times a dollar invested at 55 (at 8% real returns over 30 years).
A = P(1 + r)t — final amount equals principal times one-plus-rate to the power of years. With yearly contributions, each contribution compounds for its own remaining years. The calculator above runs this math year by year.
Divide 72 by your annual return to get the doubling time in years. 10% → 7.2 years. 7% → ~10.3 years. It's an approximation, accurate within a few percent for normal rates.
Only on paper over absurd timescales — see our time-to-trillion calculator. Real fortunes come from concentrated equity bets that the market reprices, not from compounding savings. This tool is for curiosity and education, not financial advice.
No. All figures are nominal and pre-tax. Inflation (~2-3%/yr historically) and taxes both reduce real returns substantially — subtract them mentally from any rate you enter.