Rule of 72 calculator

What is the rule of 72?

A shortcut for how long money takes to double at a yearly rate: 72 ÷ the rate. At 6% that is 72 ÷ 6 = 12 years; the exact answer is 11.9 years.

How accurate is it?

Very close for rates between about 6% and 10%: at 8% the rule says 9 years and the exact figure is 9.006. At very low or very high rates it drifts further.

What rate do I need to double in 10 years?

By the rule, 72 ÷ 10 = 7.2%; exactly, 2^(1/10) − 1 = 7.18%.

Does it work for inflation?

Yes — prices double in 72 ÷ the inflation rate years. At 3% inflation, prices double in about 24 years.

Where does 72 come from?

The exact doubling time is ln 2 ÷ ln(1 + r) ≈ 0.693 ÷ r; 72 is used instead of 69.3 because it fits typical rates better and divides evenly by many numbers.

How far off is the rule at different rates?

Here are the rule's answers against the exact ones, in years: 2%: 36.0 against 35.0; 4%: 18.0 against 17.7; 6%: 12.0 against 11.9; 8%: 9.0 against 9.0; 10%: 7.2 against 7.3; 12%: 6.0 against 6.1; 20%: 3.6 against 3.8. The two agree at a rate of about 7.85%. Below that the rule gives a longer time than the exact one, and above it a shorter time. The error is small near 8% and grows at both ends.

How do I use the rule for more than one doubling?

Count the doublings. At 8% the rule says money doubles about every 9 years, so $5,000 over 36 years doubles four times, to $80,000. The Federal Reserve Bank of St. Louis uses this example, and the exact compound figure is $79,841, so the shortcut lands close at 8%.

How the rule and the exact answer differ

Money growing at r a year doubles when (1 + r)ⁿ = 2, so the exact time is n = ln 2 ÷ ln(1 + r). For small r, ln(1 + r) is close to r, which gives n ≈ 0.693 ÷ r, or 69.3 ÷ (rate in percent). Because ln(1 + r) is slightly smaller than r, the true time is a bit longer, and using 72 in place of 69.3 corrects for that around 8%. In the other direction, the rate needed to double in n years is 72 ÷ n by the rule and 2^(1/n) − 1 exactly.

Worked example: 6%

At 6%, 72 ÷ 6 = 12 years. The exact time is ln 2 ÷ ln 1.06 = 11.90 years, so the shortcut is off by about 0.1 year, or 0.9%. At 2% the rule gives 36 years against 35.0, and at 20% it gives 3.6 against 3.8, which is why the rule is best used for mid-range rates.

Common mistakes

Entering the rate as a decimal is the most common: use 6 for 6%, not 0.06, or the rule gives 1,200 years. Applying the rule to a rate that is not compounded yearly is another, since the shortcut assumes yearly compounding and the exact figure here does too. Treating the answer as a forecast of real wealth is a third: it ignores taxes, fees and inflation, and returns are not constant. And remember that the rule is an approximation, as the Federal Reserve Bank of St. Louis says, so use the exact figure when the decision depends on it.

Sources: Federal Reserve Bank of St. Louis, Open Vault, How Compound Interest Works & How to Estimate It (Mark Catanzaro, September 12, 2018): dividing 72 by the rate, the $5,000 example over 36 years, and the statement that the rule is intended as an approximation. The exact doubling time, ln 2 ÷ ln(1 + rate), is the standard compound-growth formula. See also the compound interest calculator, the CAGR calculator and the inflation calculator.

Estimates for planning only — not financial advice. Your lender's figures decide. How we check our calculators.