Tukuk-OSInterest is money paid for the use of money; compound interest means last year’s interest starts earning too. At 10% a year, 100 becomes 110, then 121, then 133 — a curve that starts politely and ends steeply, which is why young savers underestimate it and old debtors are crushed by it. Credit cards are the negative side: 18% annual interest compounds monthly, so a balance carried all year grows about 20%, not 18% — the quoted rate systematically undersells the cost.
The Rule of 72 is the one formula worth memorising: dividing 72 by an annual percentage gives roughly how long it takes to double. At 8%, about 9 years; at 24%, 3 years; at 6% inflation, your money halves in value in 12. Accurate enough for any conversation, no calculator, works in both directions — growth and erosion.
The arithmetic of the real world: 100 a month at a typical long-run 7% return becomes roughly 122,000 after 30 years — only 36,000 of it yours, the rest growth-on-growth — while starting the same habit ten years later ends you near 58,000. Time is the dominant ingredient, not the amount; the snowball needs the hill more than the snow. Einstein’s apocryphal “greatest mathematical wonder” quote is unverified, but the exponential is not.