How Compound Interest Actually Works (With the Math That Matters)
By the Stoia team · August 10, 2026 · 6 min read
Simple interest pays you on what you put in. Compound interest pays you on what you put in plus everything it already earned, which turns growth into a snowball: small and unimpressive for years, then abruptly the biggest force in the account. Understanding exactly when and why that happens is the difference between trusting the process and quitting during the boring early stretch.
The formula, in plain English
The textbook version is A = P(1 + r/n)nt, but the plain reading is simpler: each period, the balance grows by the rate, and next period's growth is computed on the new, bigger balance. The three inputs that matter are the amount invested, the rate of return, and, above all, time. Nothing in the formula rewards intensity; everything rewards duration.
Watch the crossover happen
$500 a month at a 7% average annual return (roughly the long-run inflation-adjusted return of broad stock indexes):
| Year | You contributed | Balance | Growth's share |
|---|---|---|---|
| 5 | $30,000 | $35,800 | 16% |
| 10 | $60,000 | $86,000 | 30% |
| 20 | $120,000 | $260,000 | 54% |
| 30 | $180,000 | $606,000 | 70% |
Around year 18, the account's own growth starts out-earning the $6,000 you add each year, and it never looks back. That crossover is the whole game. Run your own numbers in the compound interest calculator and find your crossover year.
The rule of 72
Divide 72 by your annual return to estimate how many years a lump sum takes to double: at 7%, about 10 years; at 3% (a good savings account), about 24. The rule cuts both ways, though: at 20% credit card APR, a balance you ignore doubles in under 4 years. Compounding does not care which direction it is working.
The three levers, ranked
- Time. Starting at 25 instead of 35 roughly doubles the ending balance at the same contribution. No other lever comes close, which is why coast FIRE math works at all.
- Rate. Owning the market via low-cost index funds (the approach in the investing chapter of our course) historically beat cash by a wide margin, and fees compound against you exactly as returns compound for you.
- Amount. It matters, but a bigger contribution started late loses to a smaller one started early. Increasing your savings rate works best when it happens now.
Where cash fits
Compounding applies to savings accounts too, just slower: interest on an emergency fund quietly offsets some inflation while the money waits (the HYSA calculator shows the effect). The mistake is holding long-horizon money at cash rates: over decades, the gap between 3% and 7% is not a few percent, it is a multiple.
Seeing your own compounding
The chart that makes this real is your own: Stoia's net worth history plots every account daily, so the crossover stops being a table in a blog post and becomes a line you watch bend in your favor.