Compound interest, explained with real numbers
Why starting ten years earlier beats contributing twice as much, what monthly compounding actually does, and how to sanity-check any projection — including ours.
Compound interest is the one piece of financial math where intuition consistently fails, because humans think in straight lines and compounding is a curve. The numbers below are the fastest way to recalibrate.
The mechanism in one paragraph
Simple interest pays on your original money only. Compound interest pays on your money and on the interest it already earned — so each period’s growth becomes next period’s base. That feedback loop is the whole story: growth on growth, repeated.
The number that surprises everyone
Invest $500/month at a 7% annual return:
| Years | You contributed | Balance | Growth share |
|---|---|---|---|
| 10 | $60,000 | ~$86,000 | 30% |
| 20 | $120,000 | ~$255,000 | 53% |
| 30 | $180,000 | ~$588,000 | 69% |
| 40 | $240,000 | ~$1,244,000 | 81% |
Two things to notice. The last decade added more than the first three combined — the curve is steep at the end, not the start. And by year 40, four dollars out of five in the account weren’t contributed; they grew. Run your own numbers in the compound interest calculator and watch the contributions-vs-growth split.
Why starting early beats contributing more
Person A invests $300/month from age 25 to 65. Person B invests $600/month — twice as much — but starts at 40. Same 7% return:
- A: $144,000 contributed → ~$787,000 at 65
- B: $180,000 contributed → ~$486,000 at 65
B put in more money and ended with 38% less, because A’s early dollars compounded for 40 years. In compounding, time is the multiplier that money can’t buy back. This is also the idea behind Coast FIRE: save hard early enough and growth alone can carry you the rest of the way.
The rule of 72
For quick mental math: divide 72 by the annual return to get the doubling time. At 7%, money doubles every ~10 years; at 3%, every 24. It also works on costs — 2% annual fees mean the fee-drag alone halves your relative outcome over 36 years. And inflation: at 3%, prices double every 24 years, which is why long projections should always be read in “real” (inflation-adjusted) terms.
What compounding frequency changes (less than you think)
Monthly vs annual compounding sounds important, but at normal rates it’s a rounding error: $10,000 at 7% for 10 years is $19,672 compounded annually, $20,097 monthly. The variables that actually move outcomes, in order: how long, how much, at what return, and at what cost (fees compound against you with the same relentlessness).
Sanity-checking any projection
Every projection — including our calculators’ — is arithmetic on assumptions, so check the assumptions:
- Return: long-run diversified stock returns have averaged ~7% real (after inflation), but with huge year-to-year swings. Nothing guarantees the average shows up during your years.
- Sequence: the calculators compound smoothly; markets don’t. Bad early years with ongoing withdrawals behave much worse than the same average return smoothly delivered.
- Inflation: always look at the inflation-adjusted line for anything decades out — $1M in 30 years buys roughly what $400–500k buys today at ~2.5–3% inflation.
Use projections to compare decisions (save more vs start earlier vs cut fees), not to predict a specific future balance. They’re excellent at the first job and structurally incapable of the second.