The Rule of 72:
a mental shortcut for how long money takes to double

The shortcut in one line

Divide 72 by the annual growth rate, written as a whole percentage, and you get the approximate number of years needed for the amount to double. At 6% it is 12 years; at 9%, 8 years; at 12%, 6 years. No exponent keys, no spreadsheet, and the answer is good enough to settle a conversation.

The rule works for anything growing at a compound rate: a deposit, an equity index, a salary raised by a fixed percentage, or a price rising with inflation. It also works backward for decline, so a currency losing 6% a year in value halves in about 12 years.

Where 72 comes from

Doubling means (1 + r)ⁿ = 2, so the exact answer is n = ln 2 ÷ ln(1 + r). The natural log of 2 is 0.693, and for small rates ln(1 + r) is close to r itself. That gives n ≈ 69.3 ÷ (rate in percent), the so-called Rule of 69.3, which is exact for continuous compounding.

For annual compounding at the rates people meet in practice, ln(1 + r) is a bit smaller than r, so the true doubling time runs slightly longer. Adding about 2.7 to 69.3 lands at 72, which also happens to divide neatly by 2, 3, 4, 6, 8, 9 and 12. That convenience is the real reason 72 beat 69.3 in textbooks.

Some practitioners prefer 70 for low rates and 69 for continuous or daily compounding. They are the same idea with a different constant.

How accurate is it?

The next table compares the shortcut with the exact figure ln 2 ÷ ln(1 + r). The estimate is nearly perfect around 8% and drifts steadily at either end.

At rates above 20% the rule starts to understate the true time by more than two months, and it is poorly suited to rates above 40%. Below 2% the estimate runs a year or more too long, so use 70 or 69.3 there.

Worked example: ₹5,00,000 at 9%

The same trick reverses neatly. If you want money to double in six years, divide 72 by 6 and you need roughly 12% a year. If you want it to double in ten years, 7.2% is enough, which is why a 7% return is often described as doubling money roughly every decade (the exact figure is 10.2 years).

Tripling, quadrupling and halving

The shortcut family covers other multiples. Because doubling twice gives four times, the time to quadruple is about twice the doubling time, so 144 ÷ r. Tripling uses 114 ÷ r. At 8%, these give 18 years and 14.25 years against exact values of 18.01 and 14.27.

• Quadruple: 144 ÷ rate, so at 8% about 18 years.
• Triple: 114 ÷ rate, so at 8% about 14.3 years.
• Halve a purchasing-power figure: 72 ÷ inflation rate. At 6% inflation money loses half its buying power in about 12 years.
• Debt: a card balance growing at 18% a year doubles in 72 ÷ 18 = 4 years if nothing is paid, which is why unpaid high-interest balances snowball.

Using it on debt, prices and pay

The same division works on anything that compounds against you. A credit-card balance charged at 36% a year, left unpaid, doubles in about 72 ÷ 36 = 2 years. The exact figure is 2.25 years, so the shortcut is optimistic by about three months at this high rate, which again says: above 20%, add a little.

• Salary: a 6% annual raise doubles pay in about 12 years, though inflation at 5% means the real gain is under 1% a year and doubling buying power would take about 75 years.
• Population or demand: a market growing 9% a year doubles in about 8 years, a useful sanity check on a five-year forecast.
• Rent: an annual escalation of 8% doubles the rent in nine years. A ₹25,000 flat becomes ₹50,000 by year nine.

Because it is so quick, the rule is best used to test claims. A projected growth figure that implies doubling every two years deserves a closer look at the assumptions behind it.

Limits and what it hides

The rule assumes a constant return, which real investments rarely deliver. A fund that gains 20% and then loses 10% does not average 5% in any useful sense; its path matters. The rule also ignores contributions, taxes and charges, all of which push the real doubling time out.

It also fails quietly when the rate is not a clean annual number. A return quoted per month or per quarter must be converted first: 1% a month is about 12.7% a year when compounded, so the doubling time is about 5.8 years by the exact formula, not 72 ÷ 12 = 6, and certainly not 72 ÷ 1 = 72 months misread as years.

Use it for quick comparisons and for a feel of scale. If a scheme promises to double your money in four years, 72 ÷ 4 says that is an 18% annual return, which is a reason to ask hard questions. For planning, switch to the exact formula or a calculator.