The rule of 72, a quick way to see when money doubles
The rule of 72 is a shortcut for doing the math in your head. Divide 72 by the annual return, as a percentage, and you get roughly how many years it takes your money to double.
Years to double ≈ 72 ÷ annual return
If an investment returns 6% a year, 72 ÷ 6 = 12. In about 12 years, $10,000 would become $20,000. You do not need a calculator, and that is the whole point: you can use it to size up a number while someone is telling it to you.
How accurate it is
This table compares the rule with the exact value:
| Return | Rule of 72 | Exact value |
|---|---|---|
| 1% | 72 years | 69.7 years |
| 2% | 36 years | 35.0 years |
| 3% | 24 years | 23.4 years |
| 4% | 18 years | 17.7 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6 years | 6.1 years |
| 20% | 3.6 years | 3.8 years |
Between 3% and 12%, the error is only a matter of months. Outside that range it gets larger, but the rule still gives you a useful idea.
Why it works
Doubling means that (1 + r) raised to the number of years equals 2. Solving that brings in the natural logarithm of 2, which is 0.693. So for very low rates, the mathematically precise rule would be 69.3.
People use 72 for two reasons. It offsets the error at common returns of 6% to 10%, and it divides evenly by 2, 3, 4, 6, 8, 9 and 12. It is built for mental math.
Five practical uses
1. Finding the return you need. It works backward too. To double your savings in 10 years, you need about 72 ÷ 10 = 7.2% a year.
2. Spotting suspicious promises. If someone offers to double your money in two years, that takes about 36% a year, which is not believable as a safe return. The rule does not prove fraud, but it gives you a reason to dig deeper.
3. Measuring inflation. If prices rise 3% a year, they double in about 24 years. Put another way, idle money would buy half as much by then. We go further in how inflation affects your savings.
4. Seeing the real cost of debt. Unpaid credit card debt at 24% doubles in about three years. It is the same math working against you, and it explains why it makes sense to pay off expensive debt first.
5. Working out what a fee costs. An investment returning 7% doubles in about 10.3 years. If 1% goes to fees and you keep 6%, it takes 12. A single point delays each doubling by almost two years.
How many doublings you get
The rule also shows the power of time. At 6% a year, $10,000 becomes:
- $20,000 at around 12 years.
- $40,000 at around 24 years.
- $80,000 at around 36 years.
Each doubling takes the same time, but adds more money than the one before. That is why the final years of long-term saving count so much, and why starting to save early has such a big effect.
Its limits
The rule only gives a reasonable estimate under certain conditions:
- It applies to a lump sum. It does not account for regular contributions.
- It assumes a steady return. An investment with ups and downs does not grow evenly, and what counts is its compound annual growth rate, not the simple average of each year’s return.
- It ignores taxes, fees and inflation. Use the return you actually keep to get a realistic figure.
- It guarantees nothing. Except for fixed-rate products, past or expected returns may not materialize.
For an exact calculation with monthly contributions, use the compound interest calculator. To understand where this effect comes from, read how compound interest works.