How does compound interest actually work?
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tl;dr
Compound interest pays interest on past interest, so money grows in an accelerating curve. The Rule of 72 shows the speed: divide 72 by your rate to see how many years one doubling takes.
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Compound interest means your interest starts earning interest of its own. Each payout joins the original amount, so the base keeps growing and the same percentage pays a little more every cycle. That feedback loop is why savings curves bend upward — and why time matters more than the starting amount.
The loop that bends the curve
Simple interest pays on your original deposit forever — a flat line. Compound interest folds every payout back into the base, so next year's interest is calculated on a bigger number. Nothing about the rate changed; the base did. Run that loop for years and growth stops looking like addition and starts looking like a curve.
The Rule of 72
There's a centuries-old shortcut for feeling this in your head: divide 72 by the annual rate to estimate how many years one doubling takes. At 8%, money doubles in about nine years; at 6%, twelve. It's sharpest between 6% and 10%, and it makes the real lever obvious — every extra decade you leave money alone buys you another doubling, and the last doubling is always the biggest.
The fine print
The same math runs in reverse: unpaid debt compounds too, which is how a high-rate balance can double in a few short years. And the famous story that Einstein invented the Rule of 72? The rule appears in Luca Pacioli's arithmetic book from 1494 — four hundred years before Einstein was born.
cited
Sources
- [01]The Rule of 72: What Is It? — SmartAsset
“To use it, divide 72 by the annual interest rate; at an 8% annual return, your money doubles in 9 years.”
- [02]The Rule of 72 — SoFi
“The rule was recorded by Luca Pacioli in his 1494 book Summa de arithmetica — long before Einstein was born.”
people also ask
Keep asking
What's the difference between simple and compound interest?
Simple interest pays only on the original amount, forever. Compound interest folds each payout into the base, so every payout after the first is a little bigger than the last.
Why does starting early matter so much?
Time sets how many doublings you collect. At 8%, thirty years is roughly three doublings — about eight times your money — while ten years gives just one. The last doubling is always the largest.
Does compounding work against me too?
Yes — unpaid debt compounds by the same math. A balance at a 24% annual rate roughly doubles in three years if nothing gets paid down.
How accurate is the Rule of 72?
It's a mental shortcut, sharpest between 6% and 10% annual rates. Outside that range it drifts a little, but for everyday estimates it stays remarkably close to the true math.
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