Home / Calculators / Rule of 72 calculator
Rule of 72 calculator
Years for money to double at any return, by the rule of 72 and by the exact formula.
The rule of 72 says money doubles in about 72 ÷ the yearly return in years. At 8% that is 9 years; the exact answer is 9.01 years, so the shortcut is very close.
Your money doubles in about
9.0 years
Exact answer: 9.01 years, 0.01 less than the rule.
$10,000 becomes $20,000 in 9.0 years and $40,000 in 18.0 years, compounding once a year.
| Return a year | Rule of 72 | Exact | Difference |
|---|---|---|---|
| 1% | 72.0 years | 69.7 years | +2.34 |
| 2% | 36.0 years | 35.0 years | +1.00 |
| 3% | 24.0 years | 23.4 years | +0.55 |
| 4% | 18.0 years | 17.7 years | +0.33 |
| 5% | 14.4 years | 14.2 years | +0.19 |
| 6% | 12.0 years | 11.9 years | +0.10 |
| 7% | 10.3 years | 10.2 years | +0.04 |
| 8% | 9.0 years | 9.0 years | −0.01 |
| 9% | 8.0 years | 8.0 years | −0.04 |
| 10% | 7.2 years | 7.3 years | −0.07 |
| 12% | 6.0 years | 6.1 years | −0.12 |
| 15% | 4.8 years | 5.0 years | −0.16 |
The rule and the exact formula
Years to double ≈ 72 ÷ return in % · exact: ln 2 ÷ ln(1 + r)
The rule is a shortcut for the exact formula. It is most accurate between about 6% and 10%; at 2% it gives 36 years against an exact 35.0, and at 20% it gives 3.6 against 3.8.
Doubling, again and again
At 7% a year, $10,000 doubles about every 10.2 years:
| After | Balance at 7% |
|---|---|
| Today | $10,000 |
| 10.2 years | $20,000 |
| 20.5 years | $40,000 |
| 30.7 years | $80,000 |
| 41.0 years | $160,000 |
The same rule works backwards: to double in 10 years you need about 72 ÷ 10 = 7.2% a year (exactly 7.18%). It also works for costs: at 3% inflation prices double in about 24 years.
Questions people ask
What is the Rule of 72 in simple terms?
A quick way to see how long money takes to double: divide 72 by the yearly return. At 6% that is 72 ÷ 6 = 12 years; the exact answer is 11.9.
How long does 100K take to double?
It depends only on the return, not the amount: $100,000 doubles in about 14.2 years at 5%, 10.2 at 7% and 7.3 at 10%, with growth compounding once a year and nothing taken out.
Does the Rule of 72 actually work?
For typical returns it lands within a few months of the exact answer: at 8% it says 9 years and the exact figure is 9.01. Its weakness is that real returns are not steady, so it describes an average path.
Does a 401k double every 7 years?
Only at a return of about 10% a year (72 ÷ 10 = 7.2; exact 7.3 years) with no withdrawals. At 7% it takes about 10.2 years. Contributions make the balance grow faster than that, because new money is added.
Related
The compound interest calculator gives the exact balance with monthly contributions. The FIRE calculator shows when growth and saving reach your number.
Last reviewed by Asier Fernández, editor, on . Educational information only, not financial advice. How we calculate