Level 0 Investing & ETF Basics · Part 8/16

The Rule of 72: Estimating Doubling Time

By Alexander Bock, founder and data analyst

The Rule of 72 is an approximation: 72 divided by the annual return in percent gives roughly the years until a sum doubles.

• 6% → 72 / 6 = 12 years
• 8% → 72 / 8 = 9 years
• 4% → 72 / 4 = 18 years

The rule assumes a constant return, which markets never deliver. It does show how strongly a few percentage points of return or cost, and the length of the holding period, change the outcome over decades.

The savings-plan calculator gives the exact figure; the fee article shows how ongoing costs stretch the doubling time.

Where the 72 Comes From

To be exact, a sum doubles in ln 2 ÷ ln(1 + r) years, where r is the annual return as a decimal. For small returns, ln(1 + r) is roughly r, which gives 69.3 ÷ the return in percent. The 72 sits a little above that because it fits typical returns of 6% to 10% more closely. It also divides evenly by many numbers: 2, 3, 4, 6, 8, 9 and 12.

How Accurate the Rule Is

Between 4% and 12%, the rule is off by less than half a year. At very low returns it overstates the time, at high returns it understates it.

Inflation and Costs

The same arithmetic works for anything that grows at a fixed rate each year. At 2% inflation, purchasing power halves after 72 ÷ 2 = 36 years, exactly after 35. Costs translate the same way. If a fund earns 7% before costs, money doubles in about 10.5 years with 0.2% in ongoing costs (6.8% net). With 1.5% (5.5% net), it takes almost 13 years.

Limits

• The rule assumes a constant return. Swings slow growth down: a year at −20% followed by one at +20% does not add up to zero but to −4%.
• It applies to a single lump sum, not to regular contributions.
• Taxes stretch the doubling time further.

Information only, not investment advice.