The Rule of 72: How Long to Double Your Money

Quick: at 8% per year, how long until your money doubles?

Most people freeze. They reach for a calculator and end up with 9.006 years. There's a shortcut that gives you the answer in two seconds, and once you start using it you'll wonder how you ever thought about returns without it.

The rule in one line

Divide 72 by your annual rate. That's how many years it takes for your money to double.

Years to double ≈ 72 ÷ Annual rate

A handful of examples:

| Annual rate | Rule of 72 says | Exact answer | | ----------- | --------------- | ------------ | | 4% | 18 years | 17.67 years | | 6% | 12 years | 11.90 years | | 8% | 9 years | 9.01 years | | 10% | 7.2 years | 7.27 years | | 12% | 6 years | 6.12 years | | 15% | 4.8 years | 4.96 years | | 20% | 3.6 years | 3.80 years |

The shortcut is accurate to a fraction of a year across the range that actually matters in personal finance. It starts to slip at very high rates (above 30% the gap widens) and slightly undershoots at very low rates. Between 4% and 15%, it's good enough that more precision is just noise.

Where the 72 comes from

The exact doubling time at rate r (as a decimal) is:

Years = ln(2) / ln(1 + r)

For small r, ln(1 + r) is roughly r. And ln(2) is about 0.6931. So:

Years ≈ 0.6931 / r
       ≈ 69.31 / Rate%

So technically the rule should be 69.3, not 72. Two reasons it's 72 in practice:

1. 72 divides cleanly into common rates — 2, 3, 4, 6, 8, 9, 12, 18, 24. Mental math is fast.
2. It corrects for the small approximation error in ln(1 + r) ≈ r for rates around 6–10%, where most planning happens.

The constant is deliberately rounded for usability. You can verify the math on our compound interest calculator: set principal to 1, plug in any rate, watch when the balance hits 2. For any rate from 4% to 18%, the Rule of 72 prediction will be within a few months.

What it's good for

Five places the rule actually earns its keep.

Sanity-checking expected returns

Someone promising "we'll double your money in two years" is claiming a 36% annual return. The S&P 500's long-term average is around 10% nominal, which means money doubles every 7 years. The instant you hear "double in 18 months" the rule should make you ask: a 48% annual return is roughly five times what a great hedge fund delivers in a normal year. What does this person have that nobody else does?

Comparing investment options

Choosing between a savings account at 4.5% and a long-term diversified portfolio at 8%? The Rule of 72 makes it visceral: 16 years vs 9 years to double. A $10,000 deposit becomes $20,000 vs $40,000 over a typical 32-year investing lifetime. Same starting capital. Same horizon. One doubles twice, the other doubles four times.

Understanding inflation

Inflation is compounding in reverse. At 3% per year, a dollar loses half its purchasing power every 24 years. At 6%, every 12. This is why a "fixed income" pension that doesn't index to inflation quietly turns into a half-pension, then a quarter-pension. Anyone planning retirement decades out without modelling inflation is being optimistic.

Debt psychology

The rule runs against you when you owe money. A credit card at 24% APR doubles your debt every 3 years if you leave it unpaid. Pay only the minimum at that rate and watch the balance double in three years, triple in five. For loans, see our loan EMI calculator — it shows the exact monthly impact of any rate over any term.

Crypto and high-volatility assets

The rule also clarifies how aggressive your assumptions are. "Expecting" crypto to double every two years means forecasting a sustained 36% per year. Bitcoin has done this over some 4-year windows. It has also lost 80% in 12 months. The same rule that promises doubling in good scenarios tells you nothing about variance — and a rate alone is the wrong abstraction for volatile assets.

When the rule breaks

Two situations where it stops being accurate.

Continuous or daily compounding at high rates. The rule assumes annual compounding. At 12% compounded daily, doubling happens slightly faster than the rule predicts because the more frequent compounding builds on more cumulative interest. For practical retirement-planning rates compounded monthly at 6–10%, the gap is tiny.

Very high rates (above 20%). At 50% per year the rule says 1.44 years; the true answer is 1.71. The ln(1 + r) ≈ r approximation falls apart because r is no longer small. For high rates, do the direct calculation.

The rule also says nothing about how long losses take to recover. A 50% loss needs a 100% gain to break even, not 50%. The asymmetry of compounding around a negative period is the most underappreciated principle in personal investing.

Variants you'll see

The Rule of 72 has cousins that target different multiples.

• Rule of 114 — time to triple. Years to triple ≈ 114 ÷ Rate%. At 8%, money triples in about 14.25 years.
• Rule of 144 — time to quadruple. Years to quadruple ≈ 144 ÷ Rate%. At 8%, about 18 years.
• Rule of 69.3 — the technically-correct version for continuous compounding. Use it for maximum precision; most people don't bother.

All three come from the same logarithmic identity. They just substitute different multiples. The Rule of 72 dominates in popular usage because doubling is the most common reference point, and because 72 has more clean divisors than 69 or 114.

The real point

The deeper value of the Rule of 72 isn't speed at arithmetic. It's that the rule forces compounding into your intuition.

People are bad at exponential growth. We extrapolate linearly: a 10% return for one year becomes a 100% return over ten years in our heads. The real answer is 159%. The compounded number is 60% higher than the linear estimate. The longer the horizon, the bigger the gap, and the more important it is to think in doublings rather than annual percentages.

Over a 30-year working career at 8% per year, money doubles three and a bit times: $10k → $20k → $40k → $80k → roughly $100k by year 30. Linear thinking predicts $34k. The Rule of 72 gives you the right answer in three seconds: 30 years ÷ 9-year doubling time = 3.3 doublings.

That intuition matters most for people under 30, where every doubling roughly compounds for life. Money invested at 22 doubles to age 31, then 40, then 49, then 58, then 67. A $5,000 contribution at age 22 in an index fund at 8% nominal becomes roughly $160,000 by retirement, with zero additional contributions. The Rule of 72 turns that abstract claim into a concrete count: five doublings, in one working life.

To see the full table for your own situation — current age, retirement age, expected rate, monthly contributions — our retirement calculator does the precise math. But for any back-of-envelope conversation, divide 72 by the rate. You'll have the answer faster than anyone else in the room.

One number, worth remembering forever.