What is the Rule of 72 in finance?

The Rule of 72 is a quick mental math shortcut used to estimate how many years it will take for an investment to double at a given annual fixed interest rate: Years to Double ≈ 72 ÷ Annual Interest Rate.

Can you use the Rule of 72 for inflation?

Yes. Dividing 72 by the annual inflation rate tells you how many years it will take for the real purchasing power of your money to be cut in half.

Rule of 72 Explained: Mental Math for Compound Interest & Inflation

Bhavin Solanki Verified Author

Lead Developer & Quantitative Analyst

Updated: October 2026

5 min read

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The Fundamental Formula

Years to Double ≈ 72 ÷ Annual Return Rate (%)

If an equity portfolio generates an average annual return of 12%, your initial capital will double in approximately 6 years (72 ÷ 12 = 6). If a fixed deposit pays 7%, doubling takes approximately 10.3 years (72 ÷ 7 = 10.28).

1. Where Does 72 Come From? The Mathematical Proof

The standard compound interest formula is:

A = P × (1 + r)ᵗ

To find the doubling time, we set the terminal amount A = 2P:

2P = P × (1 + r)ᵗ ⇒ 2 = (1 + r)ᵗ

Taking the natural logarithm (ln) of both sides:

ln(2) = t × ln(1 + r)

Because ln(2) ≈ 0.693147, and for small values of r, the Taylor series expansion tells us ln(1 + r) ≈ r:

t ≈ 0.693 ÷ r = 69.3 ÷ (r × 100)

While 69.3 is mathematically the purest number for continuous compounding, 72 was adopted because it is divisible by numerous integers (2, 3, 4, 6, 8, 9, 12), making fast mental calculations feasible without a calculator.

2. Tripling and Quadrupling: Rules of 114 & 144

The Rule of 114

Tripling Money (3x)

Years to Triple ≈ 114 ÷ Rate (%)

Derived from ln(3) ≈ 1.0986. At a 12% return, your investment will triple in approximately 9.5 years (114 ÷ 12 = 9.5).

The Rule of 144

Quadrupling Money (4x)

Years to 4x ≈ 144 ÷ Rate (%)

Because 4x is simply doubling twice (2 × 72 = 144). At a 12% return, your wealth quadruples in approximately 12 years (144 ÷ 12 = 12).

3. The Reverse Application: Calculating Inflation Halving

The Rule of 72 works in reverse to calculate the destructive compounding of price inflation:

Years to Halve Purchasing Power ≈ 72 ÷ Annual Inflation Rate (%)

If healthcare and lifestyle inflation runs at 6% per year, ₹1 Crore will have the purchasing power of only ₹50 Lakhs in 12 years (72 ÷ 6 = 12). By Year 24, its purchasing power drops to just ₹25 Lakhs. This demonstrates why leaving savings in a bank account earning 3% is a guaranteed loss in real terms.

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Compare the Rule of 72 approximation against exact logarithmic formulas across any custom interest rate.

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