Money that earns interest, and then earns interest on THAT interest, doesn’t grow in a line — it curves upward, slowly then suddenly. A handy shortcut: divide 72 by the percentage rate and you get the years to DOUBLE. Einstein supposedly called it the eighth wonder; whether or not he did, the maths is relentless. Slide the rate and watch the doubling time drop.
Compound interest grows a principal as A = P(1+r)ᵗ: each period’s interest joins the base, so growth is EXPONENTIAL, not linear. The doubling time is ln2/ln(1+r), and for small rates that is closely approximated by the Rule of 72 — 72/(rate in %) — e.g. 6% doubles in ~12 years. Over decades the exponential dwarfs any linear saving. A fail-loud self-check throws unless the true doubling time at 6% matches 72/6 within a year and the balance more than doubles over the horizon. ◆ real finance, node-verified.
Fixed-rate annual compounding (the exact P(1+r)ᵗ); the Rule of 72 is an approximation best near 5–10% (72/r drifts at extremes), and real returns vary and carry risk — the exponential-not-linear growth and the doubling law are exact.