What makes compounding the quiet miracle of finance?
A famous quote — usually attributed to Einstein, almost certainly apocryphal — calls compound interest the eighth wonder of the world. The attribution is legend; the math underneath is not.
Interest on interest
Simple growth: €1,000 earning 7% gives €70 every year, forever — €70, €70, €70. Compound growth: each year's interest joins the principal and starts earning ITSELF. Year one: €70. Year two: 7% of €1,070 = €74.90. The increments grow — quietly at first, absurdly later.
- After 10 years: €1,000 → roughly €1,970.
- After 30 years: roughly €7,610.
- After 40 years: roughly €14,970 — nearly fifteen times the start, from a rate that never exceeded 7%.
The curve's early flatness is exactly why the miracle is "quiet" — for the first decade it looks unremarkable, and impatient observers walk away before the bend.
A long index chart is compounding drawn in public: decades of ordinary years stacking on each other — through every crash your Course 3 eyes can now spot along the way.
Time beats rate
The same table read another way: the first ten years of that forty produced €970 of growth, and the last ten produced about €7,360. So starting late is expensive in a way that feels wrong until you compute it. A saver who begins the identical 7% journey ten years later, with thirty years to run, ends at €7,610 rather than €14,970 — a decade of waiting cost half the destination. To make up those ten missing years in the remaining thirty, the late starter would need 9.4% a year instead of 7%, every year, which is not a rate anyone gets to choose.
The rule of 72
The professional's mental shortcut: 72 ÷ growth rate ≈ years to double. At 8%, money doubles in about 9 years; at 3%, about 24. It's an approximation (very accurate in the single digits), and it works in reverse for the villain's version: at 6% inflation, 72 ÷ 6 = prices double — cash halves — in about 12 years. Compounding serves whoever holds the rate: saver, lender... or the inflation eating your mattress.
Try it now
- Rule of 72, no calculator: doubling time at 4%? At 12%?
- Roughly how many DOUBLINGS did the 40-year €1,000 → €14,970 journey contain? (Hint: count the ×2s inside ×15.)
- Say it aloud: "compounding is interest earning interest — slow, then sudden."