Compound Interest and the Rule of 72

Interest on interest

Simple interest pays you on your principal only. Compound interest pays you on your principal plus every unit of interest you have already earned — and that second part is what makes long-horizon saving so powerful. The growth curve is not a straight line; it bends upward, slowly at first, then steeply.

Concretely: $10,000 at 7% compounded annually becomes about $19,700 in 10 years, $38,700 in 20 years, and $76,100 in 30 years. The first decade earns roughly $9,700; the third decade alone earns about $37,400. Same money, same rate — the difference is purely how long the interest has been earning interest.

The Rule of 72

For a quick mental estimate of doubling time, divide 72 by the annual return. At 7%, money doubles roughly every 72 ÷ 7 ≈ 10.3 years; at 4%, about every 18 years; at 12%, about every 6. The rule is an approximation of the exact logarithmic formula, and it is accurate to within a few months for rates between about 4% and 15% — exactly the range most savers care about.

The rule also works in reverse for inflation: at 3% inflation, the purchasing power of idle cash halves in about 24 years. Compounding works against you just as efficiently as it works for you.

Starting early vs contributing more

Because growth compounds over time, the calendar is a bigger lever than the contribution. Saving $500 per month at 6% (compounded monthly) for 30 years builds roughly $502,000 from the contributions alone. Wait 10 years and save the same $500 for 20 years, and the contributions build only about $231,000 — less than half, despite contributing only a third less money.

The practical takeaway is unglamorous: a modest amount started now typically beats a larger amount started later. Use the calculator to compare your own scenarios rather than trusting round-number intuition — compounding consistently defies it.

What the projection can't promise

A compound interest projection assumes a steady rate, and real investment returns are anything but steady. Treat any projected figure as a scenario, not a promise: the same monthly plan at 8% instead of 12% produces roughly 40% less after 20 years. Run the calculator at a conservative rate and an optimistic one, and plan around the gap between them.