- What's the Rule of 72 in one sentence?
- At r% compound annual growth, money roughly doubles in 72 ÷ r years. So at 8% you double in 9 years (72 ÷ 8 = 9); at 6% in 12; at 12% in 6. The actual doubling time at 8% is 9.006 years — the rule is off by about 2 days, which is why it's been the back-of-the-envelope tool of choice for 500+ years (Luca Pacioli wrote about it in 1494).
- Why does the Rule of 72 work?
- The exact compound doubling formula is years = ln(2) ÷ ln(1 + r/100). For small r, ln(1 + r/100) ≈ r/100, so years ≈ ln(2) × 100 ÷ r ≈ 69.3 ÷ r. The reason we use 72 instead of 69.3 is that 72 has more divisors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) — making the mental math clean for the rates people actually quote. The rule is most accurate at around 8%; below 4% it overstates by up to a year, above 15% it understates by more.
- When does the Rule of 72 break down?
- At very low or very high rates. At 1%, the rule says 72 years to double; the exact answer is 69.7 years. At 50%, the rule says 1.44 years; the exact answer is 1.71 years. The 6–10% sweet spot covers most realistic investment scenarios (S&P 500 historical real return ≈ 7%, nominal ≈ 10%), which is why the rule has stuck around. For extreme rates, use the exact compound formula — this calculator shows both.
- What's the Rule of 114?
- Same idea, applied to tripling. At r% compound growth, money triples in about 114 ÷ r years. 8% → 14.25 years (exact 14.27). 10% → 11.4 years (exact 11.53). The constant is bigger because tripling takes about 1.58× as long as doubling under continuous compounding — and 72 × 1.585 ≈ 114. Less famous than its cousin, but the math is identical.
- Can I use the Rule of 72 for inflation?
- Yes — and it's one of the most useful applications. Inflation compounds the same way investment returns do, just on what your money can buy instead of how much you have. At 3% inflation, the purchasing power of $1 halves in about 72 ÷ 3 = 24 years — meaning what costs $10 today will cost $20 by then. At 7% (the inflation spike of 2022), purchasing power halves in 10.3 years. The 'inflation rate' input on this calculator applies the same Rule of 72 to that direction.
- Does the Rule of 72 account for taxes, fees, or drawdowns?
- No — it's a clean-room compound-growth shortcut. Real-world investing has tax drag, fund fees, transaction costs, and volatility (the path matters, not just the average). A portfolio with a 7% expected return and 15% standard deviation does not actually double on the rule's schedule for every investor — sequence-of-returns risk can stretch doubling time substantially. Use the rule as a sanity check, not a retirement plan.
- How accurate is the Rule of 72 vs the exact formula?
- Very accurate in the equity-return range. At 6% rate the rule gives 12 years vs exact 11.90 years — off by ~5 weeks over 12 years. At 8% rate the rule gives 9 vs exact 9.01 — off by 2 days. At 10% rate the rule gives 7.2 vs exact 7.27 — off by 3 weeks. The drift becomes meaningful at the extremes: at 1% the rule overstates by 2 years (72 vs 69.7), at 20% it understates by 2 months. The calculator shows the gap on every input so you can see the magnitude before relying on the shortcut.
- Where did the Rule of 72 come from?
- The earliest known mention is in Luca Pacioli's 1494 *Summa de Arithmetica* — the same book that documented double-entry bookkeeping. Pacioli wrote: 'In wanting to know of any capital, at a given yearly percentage, in how many years it will double adding the interest to the capital, keep as a rule [the number] 72 in mind, which you will always divide by the interest.' Five centuries later, the rule still works on the same math — compound growth hasn't changed.
- Should I use Rule of 72 or Rule of 70?
- Both exist for the same purpose. Rule of 70 is slightly more accurate at low rates (where ln(2) × 100 ≈ 69.3 hugs 70 closer than 72); Rule of 72 is more accurate at typical investment rates AND has the divisibility advantage (72 is divisible by 1, 2, 3, 4, 6, 8, 9, 12 — 70 is only divisible by 1, 2, 5, 7, 10, 14). Economists tend to use Rule of 70 for population growth and inflation; finance educators tend to use Rule of 72. Functionally, the difference between them is small — the exact compound formula sits between the two, and it's the truth.
