You've probably heard that Einstein called compound interest "the eighth wonder of the world." Nobody can actually prove he said it. But a quote of dubious origin surviving for a century tells you something — compounding leaves a deep mark on people. Pair it with the Rule of 72, a bit of arithmetic anyone can do in their head, and your sense for numbers jumps a level.

Simple vs. Compound — Where the Snowballs Split

Simple interest pays you only on the original amount. Put in $10,000 at 10%, and you get $1,000 a year, every year. After 10 years: $20,000. Done.

Compound interest pays you interest on your interest. Same $10,000, same 10%, same 10 years. The result? $25,937. That's $5,937 you didn't lift a finger for.

Picture rolling a snowball. Simple interest packs on the same fistful of snow with every push. Compound interest is different: the bigger the ball gets, the more snow sticks per turn. Early on the difference is tiny. Give it time, and the gap goes exponential.

The Rule of 72 — When Does Your Money Double?

There's nothing to memorize. It's one line.

Years to double = 72 ÷ annual return (%)

Plug in some numbers:
• 3% (savings account) → 72 ÷ 3 = 24 years
• 7% (stock market average) → 72 ÷ 7 = ~10.3 years
• 10% → 72 ÷ 10 = 7.2 years
• 15% → 72 ÷ 15 = 4.8 years

A 3% savings account takes 24 years to double your balance. A 7% historical stock-market average got there in about 10. Same money, 14 years apart. Just remember this is math on paper — real stock returns aren't guaranteed, and they go through stretches of loss.

Starting at 25 vs. 35 — A 10-Year Head Start

The thing that matters most in compounding isn't the return. It's when you start. Let me show you with numbers exactly how brutal that can be.

Scenario A — say you start at 25. $250 a month for 35 years, assuming a 7% annual compounding rate. You actually put in $105,000 of your own money. The theoretical total comes out to ~$430,000.

Scenario B — same person, but starting at 35. $250 a month for 25 years, same 7% assumption. You contribute $75,000. The total: ~$200,000.

Here's what trips everyone up. Scenario A only put in $30,000 more than B. Yet under the same 7% assumption, the gap between them is ~$230,000. All from starting 10 years earlier. Again — this is an arithmetic illustration. Real markets swing, fees and taxes eat in, and losses happen.

Warren Buffett's Secret — 99% of His Wealth Came After 50

Warren Buffett is worth roughly $130 billion. The part nobody expects: over 99% of it piled up after he turned 50. It grew as he moved through his 60s, 70s, and 80s.

Buffett bought his first stock at 11 and held a ~20% annual return for 60+ years. This is where people misread him. His genius isn't the 20% — it's keeping that compounding running, uninterrupted, for an absurdly long time.

Run the counterfactual. If Buffett had started at 30 instead of 11, at the exact same return rate, his fortune would be just 0.4% of today's. Those 19 extra years account for 99.6% of the whole thing.

So What Does Compounding Look Like in Real Life

1. Dollar-cost averaging into index ETFs (illustrative) — Auto-investing a fixed amount each month into a broad index ETF like the S&P 500 gets cited a lot as the simple way to ride the market. Historical averages tend to cluster around 7–10%. Not a guaranteed number, though, and your capital can take a hit.

2. Dividend reinvestment (illustrative) — Feed the dividends you receive right back in, and they compound alongside the principal — at least in past records.

3. The real key: consistency — Keep buying the same amount even when the market drops. When prices fall, that fixed amount buys you more shares, which has tended to work in your favor over the long haul. An observed pattern, not a promise.

Curious how sharp your feel for past returns actually is? Take a round of the AI Price Sense Battle — strictly educational.