How to Calculate Compound Interest in Your Head (The Rule of 72)

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Quick answer: Divide 72 by the annual percentage rate to get the approximate number of years it takes something to double. At 6%, money doubles in about 12 years. At 9%, about 8 years. At 3% inflation, prices double in about 24 years. It’s most accurate between 6% and 10%.

Compound interest is the most important piece of arithmetic most people never do. The Rule of 72 lets you do it in your head in the time it takes a salesman to finish his sentence. Is a credit card at 24% really that bad? 72 ÷ 24 = 3: the balance doubles every three years if you don’t pay it down. How about an index fund averaging 8%? 72 ÷ 8 = 9: your money doubles roughly every nine years, which is four doublings (16×) over a 36-year career.

How to do it

1. Take the rate as a whole number. 8% → 8.
2. Divide 72 by it. 72 ÷ 8 = 9.
3. That’s the doubling time in years. About 9 years.
4. Count doublings. Over 27 years that’s 3 doublings: $10,000 → $20,000 → $40,000 → $80,000.

You can run it backwards too. Want to double your money in 6 years? 72 ÷ 6 = 12, so you’d need about 12% a year.

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<h3>Rule of 72 vs. the exact answer</h3>
<p class="sub">Set a rate and a starting amount. The chart shows the growth and marks each doubling.</p>
<div class="row">
  <div><label>Annual rate: <b id="rv">8</b>%</label><input id="r" type="range" min="1" max="30" step="0.5" value="8"></div>
  <div><label>Starting amount ($)</label><input id="p" type="number" value="10000" min="1" step="100"></div>
  <div><label>Years: <b id="yv">36</b></label><input id="y" type="range" min="5" max="60" value="36"></div>
</div>
<div class="row" style="margin-top:10px">
  <div><div class="muted">Rule of 72 says it doubles in</div><div class="big" id="est">9.0 yrs</div></div>
  <div><div class="muted">Exact (annual compounding)</div><div class="big" id="ex">9.0 yrs</div><div class="muted" id="err"></div></div>
  <div><div class="muted">Value after <span id="yv2">36</span> years</div><div class="big" id="fv">$0</div></div>
</div>
<svg id="ch" viewBox="0 0 600 220" width="100%" role="img" aria-label="Growth chart"></svg>
<div class="src">Exact doubling time = ln 2 ÷ ln(1 + r). The chart assumes a constant rate, compounded yearly, with nothing added or withdrawn.</div>
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function money(v) { return v >= 1e6 ? '$' + (v / 1e6).toFixed(2) + 'M' : '$' + Math.round(v).toLocaleString('en-US'); }
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Why it works

Money growing at rate r per year doubles when (1 + r)ᵗ = 2, which gives t = ln 2 ÷ ln(1 + r). For small rates, ln(1 + r) is close to r, so t ≈ 0.693 ÷ r, or 69.3 divided by the rate in percent. That’s the exact rule for continuous compounding. With yearly compounding the true number creeps upwards as the rate rises: it’s exactly 72 at about 7.85%. Beyond the maths, 72 also has a lot of divisors (2, 3, 4, 6, 8, 9, 12, 18, 24, 36), so it’s easy to divide in your head.

Where it breaks

• Very high rates. At 50% it says 1.4 years; the real answer is 1.7. Use it as a ballpark only.
• Very low rates. At 1% it says 72 years; the real answer is 69.7. Use 70 instead.
• Rates that change. Stock returns aren’t constant from year to year, so treat an “average 8%” doubling time as a rough guide, not a promise.

Other rules of thumb in the same family

• Rule of 70: better for low rates such as inflation and population growth.
• Rule of 114: divide 114 by the rate to estimate the time to triple.
• Rule of 144: divide 144 by the rate to estimate the time to quadruple. That’s just two doublings.

Frequently asked questions

What is the Rule of 72?

Divide 72 by the annual percentage rate to estimate how many years it takes an amount to double.

How accurate is it?

Very accurate from about 6% to 10%. It’s exact near 7.85%.

Can I use it for inflation?

Yes. At 3% inflation, prices double in about 24 years.

Why 72 and not 70?

72 is close to the true value for typical annual rates and divides evenly by lots of small numbers.

• Also see: How to Read Binary (and Count to 1,023 on Your Fingers)
• Also see: How to Measure the Height of a Tree Without Climbing It