Rule of 72: What it Is and How to Use It

The Rule of 72 is a simple mental-math shortcut for estimating how long it takes for an amount to double at a given annual compounded growth rate — or alternately, the annual rate required to double an amount over a given number of years.

How the rule works

• Years to double = 72 / (annual rate as a percent)
  Example: At 8% annual compounded growth, doubling time ≈ 72 / 8 = 9 years.

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• Annual rate (percent) ≈ 72 / (years to double)
  Example: To double in 12 years you need ≈ 72 / 12 = 6% per year.

Important notes:
– Enter the rate as a whole-number percent (8, not 0.08).
– The Rule of 72 assumes compound growth (annual compounding). It does not apply to simple interest.
– For precise results, use a calculator or the exact formula: t = ln(2) / ln(1 + r), where r is the rate in decimal form.

Common uses and examples

The Rule of 72 applies to any quantity that grows (or shrinks) exponentially:
– Investment growth: 8% → doubles in ≈ 9 years (72 / 8).
– GDP or population: 4% → doubles in ≈ 18 years (72 / 4).
– Fees and expenses: A 3% annual fee reduces growth so that principal is halved in ≈ 24 years (72 / 3).
– Debt: A 12% interest rate doubles what you owe in ≈ 6 years (72 / 12). At 20% it doubles in ≈ 3.6 years (72 / 20).
– Inflation: 6% inflation halves purchasing power in ≈ 12 years (72 / 6).

Limitations and adjustments

• Accuracy is best for interest rates roughly between 6% and 10%. Outside that range, the Rule of 72 becomes less precise.
• A simple adjustment: for each 3 percentage points a rate differs from 8%, add or subtract 1 from the numerator (so higher rates use a slightly larger numerator, lower rates a slightly smaller one). For continuous or very frequent compounding, a numerator near 69.3 gives a closer approximation; some people round that to 69 or 70 for ease of calculation.
• For exact doubling times with non-annual compounding, use the exact logarithmic formula or a financial calculator.

Origin

The Rule of 72 is an old heuristic cited as far back as 1494 in Luca Pacioli’s Summa de Arithmetica. Its long history reflects its usefulness as a quick approximation.

Practical takeaway

The Rule of 72 is a handy, quick way to understand the power of compound growth — whether estimating investment returns, the impact of fees, inflation’s effect on purchasing power, or how fast debt can grow. Use it for fast mental estimates, and rely on precise formulas or calculators when accuracy matters.