The Rule of 72 is the single most useful mental math shortcut in finance: divide 72 by an annual rate to estimate how long something takes to double. This guide covers the formula, why 72 (and not 69.3), how accurate it is, and where to apply it.

Run live numbers with our Rule of 72 calculator.

The Formula

**Years to double ≈ 72 ÷ annual rate (%)**. At 8%: 72 ÷ 8 = **9 years**. At 10%: **7.2 years**. At 3% inflation: purchasing power halves in **24 years**.

Where 72 Comes From (and Why 69.3 Is Exact)

The exact doubling time is ln(2) / ln(1 + r). Because ln(2) ≈ 0.693, the precise constant is **69.3** for continuous compounding. 72 is used because it divides evenly by 1–9 and 12, making mental math easy — a deliberate trade of a hair of precision for usability.

At higher rates, use **Rule of 73**; at very low rates, **Rule of 69.3** or 70 is slightly better.

Accuracy by Rate

  • •2% → Rule says 36 yrs, actual 35 (off ~3%).
  • •8% → Rule says 9.0, actual 9.01 (essentially perfect).
  • •15% → Rule says 4.8, actual 5.0 (use Rule of 73).
  • •Most investing/savings rates sit in the 6–10% sweet spot where 72 is near-exact.

Beyond Investing: Debt & Inflation

  • •**Credit card at 24% APR:** balance doubles in ~3 years on minimum payments — a powerful reason to pay aggressively.
  • •**Inflation at 3%:** prices double in ~24 years, silently halving purchasing power.
  • •**Salary at 5%/yr:** income doubles in ~14.4 years without promotions.
  • •**2% AUM fee:** over ~36 years, fees consume roughly half your potential growth — why low-cost matters.

Rule of 72 vs CAGR

The Rule of 72 estimates doubling time from a single rate; CAGR measures the actual annualized return of an investment that grew from one value to another. Use 72 for quick intuition, CAGR for reporting real performance.