Why 72 and not another number?

72 gives a good approximation of ln(2) ÷ r because it's highly divisible (by 2, 3, 4, 6, 8, 9, 12) making mental math easy. For precise calculations use ln(2)/ln(1+r). 70 and 69.3 (≈ln(2)×100) are also used for quick estimates.

Can the Rule of 72 be used for inflation?

Yes. At 4% inflation, purchasing power halves in 72÷4 = 18 years. This is why central banks target 2% inflation — at 2%, purchasing power halves in 36 years; at 4% inflation, it halves in just 18 years.

What is the Rule of 114 and Rule of 144?

Rule of 114: divide 114 by the rate to find years to triple your money. Rule of 144: divide 144 by the rate to find years to quadruple your money. Example at 8%: double in 9yr (72/8), triple in ~14yr (114/8), quadruple in 18yr (144/8).

● Mental math for compounding

Rule of 72 Calculator

Divide 72 by your annual return rate to see how many years it takes to double your money. Works for investments, debts, and inflation.

The Rule of 72: at 6% annual return, money doubles in 72÷6 = 12 years. At 9%, it doubles in 8 years. At 2% inflation, purchasing power halves in 36 years. This simple rule is one of the most useful mental shortcuts in personal finance.

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Results

Years to double (Rule of 72)

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Exact years (ln formula)

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Rule of 72 accuracy

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$10,000 becomes after doubling

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Years to triple (Rule of 114)

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Years to 10× (Rule of 240)

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Doubling time by rate

Rate (%/yr)	Rule of 72 (years)	Exact (years)	What $10,000 becomes

How it's calculated

The Rule of 72: mental math for compounding

The Rule of 72 is a quick way to estimate how many years it takes for an investment to double: simply divide 72 by the annual percentage rate. At an 8% return, money doubles in roughly 72 ÷ 8 = 9 years; at 6% it takes about 12 years. No calculator, no logarithms — just one division you can do in your head.

It works because compound growth follows an exponential curve, and 72 is a handy stand-in for the exact mathematical constant (ln(2) × 100 ≈ 69.3) that governs doubling. The approximation is most accurate for everyday rates between roughly 6% and 10%, staying within about 1–2% of the precise answer for the whole 3%–25% range. At very high rates it drifts, so for those you should fall back on the exact logarithmic formula.

The rule also runs in reverse: divide 72 by the number of years you have to find the annual rate you'd need. If you want to double your money in 9 years, you need about 72 ÷ 9 = 8% per year. The same logic applies to anything that grows or shrinks at a steady rate, including inflation eroding your purchasing power.

The rule approximates the logarithmic formula for doubling time by using 72 as a convenient divisible constant close to ln(2) × 100 ≈ 69.3.

Rule of 72: Doubling years ≈ 72 ÷ rate(%) Exact formula: Doubling years = ln(2) ÷ ln(1 + rate) = 0.6931 ÷ ln(1 + rate) For tripling: 114.3 ÷ rate For 10×: 230.3 ÷ rate (ln(10) × 100)

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Rule of 72: Mental shortcut: 72 ÷ annual rate = years to double. Accurate within 1-2% for rates 3%–25%.
Compounding: Earning returns on previous returns. The "72" captures this exponential growth pattern.
Doubling time: The number of periods needed for an investment to grow to twice its initial value at a constant growth rate.
Annual rate: The yearly percentage growth applied to your balance, such as an investment return or an interest rate. It is the number you divide 72 by.
Rule of 70 / 69: Variants of the same idea using 70 or 69.3 instead of 72. They are slightly more precise (69.3 ≈ ln(2) × 100) but 72 is preferred because it divides evenly by more numbers.

Disclaimer: the Rule of 72 is an approximation for educational purposes. Actual investment returns vary and are not guaranteed.

Frequently asked questions

What is the Rule of 72?

The Rule of 72 is a mental math shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6%, money doubles in 12 years. At 9%, in 8 years. It works well for rates between 3% and 25%.

Why 72 specifically?

72 is a good approximation of ln(2) × 100 ≈ 69.3, and it has the advantage of being highly divisible (by 2, 3, 4, 6, 8, 9, 12) — making mental math easy. Using 70 is slightly less accurate but even easier to divide. 69.3 is most mathematically precise.

Can the Rule of 72 apply to inflation?

Yes — divide 72 by the inflation rate to find when purchasing power halves. At 4% inflation: 72÷4 = 18 years. This is why keeping cash under a mattress is harmful during inflation — your savings lose half its value in less than 20 years at modest inflation.

Is the Rule of 72 accurate?

Very accurate for rates 3%–25%. At 8%, Rule of 72 gives 9 years vs the exact 9.006 years — less than 0.1% error. At extreme rates (50%, 100%), the error grows — use the exact logarithm formula instead.