The Rule of 72: how fast does your money double?

CostMe Research Desk · June 30, 2026

There is a piece of mental arithmetic so useful that investors, economists, and financial educators have passed it around for over a century. It fits in one sentence: divide 72 by the annual interest rate and you get the approximate number of years it takes for a quantity to double. That is the Rule of 72.

The rule is an approximation, not a proof. It works because of a property of the natural logarithm: the exact doubling time is ln(2) divided by the rate, and ln(2) is approximately 0.693. Replacing 0.693 with 72 divided by 100 is a convenient rounding that stays accurate within a few percent for rates between 2% and 25%. The arithmetic becomes easy enough to do in your head, which is the point.

Example one: savings at market return

The long-run average annual return of the U.S. stock market has been roughly 10% before inflation. Applying the Rule of 72: 72 divided by 10 equals 7.2. Money invested at that average rate doubles roughly every 7.2 years.

A $10,000 investment at 10% becomes $20,000 in about 7 years, $40,000 in about 14 years, $80,000 in about 21 years, and $160,000 in about 28 years. Each doubling period stacks on the last. This is why the later years of compounding produce such large gains in absolute dollar terms even though the rate has not changed.

Example two: credit card debt

The same rule applies to debt, but in the direction that works against you. A credit card with a 24% annual percentage rate: 72 divided by 24 equals 3. An unpaid balance doubles in about three years.

A $3,000 balance left untouched at 24% APR would grow to approximately $6,000 in three years, $12,000 in six years, and $24,000 in nine years. No additional spending, just the compounding of the existing balance. The rate that feels manageable in month one becomes the engine of a growing problem over years.

This is why the advice to pay more than the minimum on high-rate debt is not primarily about the payment amount. It is about interrupting the doubling cycle before it accelerates.

Example three: inflation

Inflation erodes purchasing power at a compound rate, which means the Rule of 72 applies there too. At 3% annual inflation: 72 divided by 3 equals 24. Prices roughly double every 24 years.

This has a direct implication for cash held in a zero-yield account. If inflation runs at 3% and your savings account yields 0.5%, the effective rate at which your purchasing power declines is about 2.5% per year. At 2.5%, the Rule of 72 gives a doubling time of about 29 years for the gap. In other words, the gap between what your cash can buy today and what it can buy in 29 years roughly doubles.

You can read more about the mechanics of this in the article on how inflation quietly shrinks savings.

Where the rule breaks down

The Rule of 72 is less accurate at very low rates (below 2%) and very high rates (above 25%). At 1%, the exact doubling time is about 69.7 years, but the rule gives 72. At 35%, the exact doubling time is about 2.3 years, but the rule gives 2.06. The error is small enough to be useful for mental estimates but worth knowing if precision matters.

The rule also assumes a constant rate, which real investments never have. It is most useful as a rough intuition builder, not as a planning calculator. For actual financial projections, a spreadsheet or dedicated tool is more appropriate.

How CostMe helps with this

The Rule of 72 is a mental shortcut for the same math that CostMe runs on every price you enter. At a 10% long-run average, a dollar roughly doubles three times in 21 years, reaching about eight times its starting value. When CostMe shows the 30-year projected value of a purchase, the Rule of 72 is the intuition pump behind that number. Explore it at the pricing page.

The science behind it

The rule's mathematical basis is the continuous compounding formula. The exact doubling time T satisfies 2 = e^(rT), giving T = ln(2)/r. Since ln(2) is approximately 0.693, using 0.72 (or 72 divided by the percentage rate) gives a slightly high estimate that partially corrects for the difference between continuous and annual compounding.

Benzion, U., Rapoport, A., and Yagil, J., 1989, "Discount Rates Inferred from Decisions: An Experimental Study," Management Science. Established that individuals systematically apply inconsistent and often very high implicit discount rates to financial decisions, which is part of why tools like the Rule of 72 that make long-run growth concrete can shift decision-making.

Stango, V. and Zinman, J., 2009, "Exponential Growth Bias and Household Finance," Journal of Finance. Documented the practical financial costs of failing to accurately estimate compound growth, finding that the bias was associated with higher borrowing costs and lower savings rates.

This is general education, not financial advice.