Rule of 72

The Rule of 72 is a mental-math shortcut for estimating how long it takes for an investment to double in value at a given fixed annual return rate. The formula is simply:

Years to double ≈ 72 ÷ annual return rate (%)

So an 8% return doubles money in roughly 9 years. A 6% return takes about 12 years. A 12% return takes about 6.

Why it works

The exact doubling-time formula is ln(2) / ln(1 + r) — natural logarithm of 2 divided by natural logarithm of one plus the rate. For small rates, this approximates to 0.693 / r (where r is expressed as a decimal). Substituting r in percent terms, that’s 69.3 / r%.

The Rule of 72 substitutes 72 for 69.3 because 72 has many more whole-number divisors than 69 — making the mental arithmetic easier. The slight overshoot also happens to compensate for the small underestimate that comes from approximating ln(1 + r) with r, so the rule is more accurate than a naive look at the math suggests.

Accuracy

The rule is most accurate for rates between 6% and 10%, where the approximation error is well under 0.1 years. It remains useful for rates between roughly 4% and 15%. Beyond that range — particularly above 20% or below 2% — the exact formula should be preferred for any precision-sensitive use.

Practical uses

• Compounding intuition — quickly comparing investments by doubling speed.
• Inflation projection — at 3% inflation, prices double in 24 years.
• Salary growth — a 4% annual raise doubles income in 18 years.
• Reverse use — to double money in 10 years, you need 7.2% (rule) or 7.18% (exact).

Limitations

The rule assumes a constant rate of return. Real-world investments rarely produce smooth annual returns, so the rule gives an order-of-magnitude estimate, not a guarantee. It also assumes annual compounding; more frequent compounding produces slightly faster doubling.

Despite these caveats, the Rule of 72 remains one of the most useful pieces of mental math in personal finance — fast enough for cocktail-party conversations, accurate enough for serious planning at typical investment-rate ranges.