Compound interest is interest paid on interest. It sounds like a technicality, and for the first few years it basically is. Give it a decade and it becomes a noticeable force. Give it three decades and it becomes the whole game. This is the math that makes patient investors rich and impatient ones poor.
Simple vs compound, in numbers
Simple interest is 7% of $10,000 = $700 per year, forever. After 30 years, you've earned $21,000 in interest and your balance is $31,000.
Compound interest pays 7% on the whole growing balance. Year one you earn $700, same as simple. Year two you earn 7% of $10,700, which is $749. Year three, 7% of $11,449 = $801. Each year's interest is a little bigger than the last because the base it's calculated on grew.
After 30 years of 7% compounding, $10,000 becomes $76,123. That's $66k in interest alone — more than triple the simple-interest outcome. The formula:
A = P(1 + r/n)^(nt)
Where P is starting principal, r is the annual rate, n is compounding periods per year, and t is years. You don't need to memorize this. The point is just that the exponent — nt — means time is doing exponential work, not linear work.
Why the first years feel slow
Here's the honest part: compounding is visibly boring for the first 5–10 years. On a $10,000 starting balance at 7%, year one adds $700. Year two, $749. Year three, $801. You could save that much by skipping a dinner out. The curve is nearly linear early on.
It starts bending around year 10. By year 15 it's obvious. By year 20 the curve is vertical-looking. The annual interest at year 30 on our example is ~$5,300 — more than half your original principal, every year, earned passively. That's what people mean by "the eighth wonder of the world."
Enter principal, monthly contribution, rate, and years. Get a year-by-year projection.
The three levers
Only three things drive the ending balance:
- Starting principal — matters, but less than you'd think over long horizons.
- Monthly contributions — usually the dominant factor for most people. $500/month for 30 years at 7% grows to ~$612,000.
- Time — the multiplier on everything. 30 years at 7% doubles your money three times. 40 years doubles it four times.
Rate of return matters too, but it's hard to control. The levers you actually pull are how much and how long.
The Rule of 72
Here's the shortcut. Divide 72 by your annual rate to estimate the doubling time:
- At 4% — money doubles every 18 years.
- At 6% — every 12 years.
- At 7% — every ~10 years.
- At 10% — every ~7 years.
- At 24% (credit card) — every 3 years. In both directions.
It's an approximation (the exact value is ln(2) / rate, ~69.3%), but the 72 version is accurate enough for any mental math and trivially easy to divide. Use it constantly.
The expense ratio trap
Compounding works against you the same way it works for you. A 1% expense ratio on a mutual fund compounds every year. Over 30 years, a 1% annual drag on a 7% return turns a $500k ending balance into ~$380k — you gave up $120k to fees you probably never saw.
This is why low-cost index funds (0.03–0.2% expense ratios) consistently beat actively managed funds (0.5–1.5%) over long horizons. Not because the managers are bad, but because the compounding drag is brutal. A 1% difference looks small on the brochure. It's gigantic on a 30-year horizon.
Starting balance, monthly contribution, rate, years. Watch the curve bend.