Rule of 72 Explained

The shortcut

To find how many years money takes to double at a given annual rate, divide 72 by the rate (in percent):

Years to double ≈ 72 / r

And the inverse direction also works:

Required rate ≈ 72 / Years

Why 72?

The exact constant for continuous compounding is ln(2) ≈ 69.3. For most realistic rates the right constant is around 70–72. 72 wins as a default because it has many small divisors — 2, 3, 4, 6, 8, 9, 12 — so it is easy to do in your head.

Where it breaks

The shortcut is accurate to about ±1% for rates between 5% and 12%. Outside that range:

• At 2%, the rule says 36 years; the exact answer is 35 years.
• At 20%, the rule says 3.6 years; the exact answer is 3.8.

For everyday questions, the error is too small to care about.

Variants worth knowing

• Rule of 70 — slightly more accurate at low rates.
• Rule of 114 — to triple instead of double.
• Rule of 144 — to quadruple.