The Rule of 72 explained

A one-second formula that does more work than you’d expect

If you’ve spent any time around investors, you’ve probably heard the Rule of 72. It’s the kind of thing that sounds too simple to be useful — and that’s exactly why it’s so good. Divide 72 by your expected annual return rate, and you have a fairly accurate estimate of how many years it will take your investment to double. That’s the entire formula. No spreadsheets, no logarithms, no app required.

At 8%, your money doubles in roughly 9 years. At 6%, about 12. At 12%, about 6. The math is so quick you can do it in conversation, which is precisely why financial educators and analysts have used it for centuries.

How the rule works

The exact formula for doubling time at a fixed rate is:

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

where r is the rate as a decimal (so 8% becomes 0.08). The natural logarithm of 2 is approximately 0.693, and for small rates ln(1 + r) ≈ r. The doubling time is therefore approximately 0.693 / r — or 69.3 / r% if you express r as a percent.

The Rule of 72 substitutes 72 for 69.3. Why? Because 72 has many more whole-number divisors than 69 (72 ÷ 2, ÷ 3, ÷ 4, ÷ 6, ÷ 8, ÷ 9, ÷ 12 are all whole numbers) — and most rates investors actually use fall into those tidy divisor slots. The slight overshoot from using 72 instead of 69.3 also happens to compensate for the small underestimate that comes from approximating ln(1 + r) with r — the two errors partially cancel.

When it’s accurate, and when it isn’t

The Rule of 72 is most accurate for rates between 6% and 10%. In that band, the approximation is within about 0.1 years of the exact answer.

Outside that band, the rule starts to diverge slightly:

• At 4%, the exact doubling time is 17.67 years; the rule says 18 — close enough.
• At 12%, exact is 6.12 years; rule says 6 — the small understatement.
• At 20%, exact is 3.80 years; rule says 3.6 — a 0.2-year gap.
• At 100%, exact is exactly 1 year; rule says 0.72 — clearly off.

For practical investment rates (5%–15%) the rule is plenty accurate. For unusually high rates or formal financial modelling, use the exact formula.

Practical applications

Inflation impact on savings. Use the rule on inflation rate to estimate when prices double. At 3% inflation, prices double in 24 years — meaning today’s $100,000 will buy roughly $50,000 worth of goods in 2050.

Comparing investment options. A fund returning 6% doubles in 12 years. A fund returning 9% doubles in 8 years. Even a 3-percentage-point difference compresses doubling time dramatically — and the gap widens further for the second doubling, the third, and so on.

Intuiting compounding power. The milestone table — 2× at one period, 4× at twice that period, 8× at three — makes the multiplicative nature of compounding obvious. At 8%, money doubles in 9 years, quadruples in 18, becomes 8× in 27, and 16× in 36. Every doubling is the same number of years, regardless of how much you started with.

Reverse use: target rate. If you need to double a particular amount in a specific time, the rule reverses cleanly. To double in 10 years, you need 7.2%. In 8 years, you need 9%. In 5 years, you need 14.4% — a rate the rule itself flags as outside the typical sustained-return range.

A useful caveat

The Rule of 72 assumes a constant rate of return — which the real world rarely provides. Stock markets average 7%–10% over long periods, but the path is anything but smooth. The rule gives you an order-of-magnitude estimate for planning, not a guarantee.

It also assumes annual compounding. If interest compounds monthly or continuously, the effective rate is slightly higher and doubling time is slightly shorter — usually a small enough effect to ignore in mental math.

Why it endures

The rule’s longevity has a simple explanation: it produces useful answers in less time than it takes to find your phone. For decisions about which fund to choose, what salary growth means over a career, or how long a pension pot will last, the Rule of 72 gives investors enough signal to make sensible choices — and frees them from the false precision of decimal-place spreadsheets when the underlying assumptions are themselves rough.

Try the calculator

Run your own numbers through our Rule of 72 calculator to see both the approximation and the exact answer side by side. Combine it with our compound interest calculator for the full picture: doubling time gives you the headline, compound projection gives you the year-by-year detail.