The rule
At 4 percent, 18 years. At 6 percent, 12. At 8 percent, 9. At 12 percent, 6. The rule works because 72 has many small divisors, so most everyday rates give a whole number of years without a calculator. It assumes compounding: the growth each year is applied to the already-grown amount, which is how interest, investment returns and price rises behave. The compound interest calculator shows the same thing year by year, with the exact doubling time for any rate.
Where the 72 comes from
An amount doubles when (1 + r)t = 2, where r is the rate as a decimal and t the number of years. Taking logarithms gives the exact answer:
For small rates, ln(1 + r) is very close to r itself, so t ≈ 0.693 ÷ r, or 69.3 divided by the rate in percent. That is the rule of 69.3, and it is exact for continuous compounding. For yearly compounding, ln(1 + r) is a little smaller than r, which makes the true doubling time a little longer than 69.3 ÷ r. Raising the constant corrects for that, and the correction grows with the rate: the best constant is about 70 at 2 percent, 72 at 8 percent and 76 at 20 percent. 72 is the choice that stays within a few months of the truth across the rates most people meet, and it divides neatly.
How accurate it is
The table compares the rule of 72 with the exact doubling time for yearly compounding, alongside the rule of 70 and the refined rule 69.3 ÷ rate + 0.35, which is the version to use when you want to be within a few weeks at any rate up to 20 percent. The differences are in years.
| Yearly rate | Exact | 72 ÷ rate | Error | 70 ÷ rate | Error | 69.3 ÷ rate + 0.35 | Error |
|---|---|---|---|---|---|---|---|
| 1% | 69.7 yrs | 72.0 | +2.3 | 70.0 | +0.3 | 69.6 | −0.0 |
| 2% | 35.0 yrs | 36.0 | +1.0 | 35.0 | −0.0 | 35.0 | −0.0 |
| 3% | 23.4 yrs | 24.0 | +0.6 | 23.3 | −0.1 | 23.4 | +0.0 |
| 4% | 17.7 yrs | 18.0 | +0.3 | 17.5 | −0.2 | 17.7 | +0.0 |
| 5% | 14.2 yrs | 14.4 | +0.2 | 14.0 | −0.2 | 14.2 | +0.0 |
| 6% | 11.9 yrs | 12.0 | +0.1 | 11.7 | −0.2 | 11.9 | +0.0 |
| 7% | 10.2 yrs | 10.3 | +0.0 | 10.0 | −0.2 | 10.3 | +0.0 |
| 8% | 9.0 yrs | 9.0 | −0.0 | 8.8 | −0.3 | 9.0 | +0.0 |
| 9% | 8.0 yrs | 8.0 | −0.0 | 7.8 | −0.3 | 8.0 | +0.0 |
| 10% | 7.3 yrs | 7.2 | −0.1 | 7.0 | −0.3 | 7.3 | +0.0 |
| 12% | 6.1 yrs | 6.0 | −0.1 | 5.8 | −0.3 | 6.1 | +0.0 |
| 15% | 5.0 yrs | 4.8 | −0.2 | 4.7 | −0.3 | 5.0 | +0.0 |
| 18% | 4.2 yrs | 4.0 | −0.2 | 3.9 | −0.3 | 4.2 | +0.0 |
| 20% | 3.8 yrs | 3.6 | −0.2 | 3.5 | −0.3 | 3.8 | +0.0 |
| 24% | 3.2 yrs | 3.0 | −0.2 | 2.9 | −0.3 | 3.2 | +0.0 |
| 36% | 2.3 yrs | 2.0 | −0.3 | 1.9 | −0.3 | 2.3 | +0.0 |
Between 4 and 12 percent the rule of 72 is within about 0.3 years of the exact figure, which is better than anyone can forecast a return. Below 3 percent it slightly overstates the time and the rule of 70 is closer; above 15 percent it understates it. At 36 percent the rule says 2.0 years and the exact answer is 2.3.
Tripling, quadrupling and more
The same logic gives a constant for any multiple: ln(multiple) ÷ ln(1 + r), fitted at 8 percent. Tripling takes about 114 ÷ rate years, quadrupling 144 ÷ rate, which is simply doubling twice. The table shows the constant and the exact years at 6 and 8 percent.
| Grow to | Rule | Exact at 6% | Exact at 8% |
|---|---|---|---|
| 3× the amount | 114 ÷ rate | 18.9 yrs | 14.3 yrs |
| 4× the amount | 144 ÷ rate | 23.8 yrs | 18.0 yrs |
| 5× the amount | 167 ÷ rate | 27.6 yrs | 20.9 yrs |
| 10× the amount | 239 ÷ rate | 39.5 yrs | 29.9 yrs |
A long horizon is where these add up. At 7 percent money doubles in about 10 years, so 40 years is four doublings: 1 becomes 2, 4, 8, 16. The CAGR calculator works the other way round, from a start value, an end value and the years in between to the steady yearly rate that connects them.
The rule in reverse
Dividing 72 by a number of years gives the rate needed to double in that time. The exact rate is 21/years − 1.
| Double in | 72 ÷ years | Exact rate |
|---|---|---|
| 5 years | 14.4% | 14.87% |
| 10 years | 7.2% | 7.18% |
| 15 years | 4.8% | 4.73% |
| 20 years | 3.6% | 3.53% |
| 25 years | 2.9% | 2.81% |
| 30 years | 2.4% | 2.34% |
| 40 years | 1.8% | 1.75% |
This is the form that answers a planning question: if a goal is twice what you have today and you want it in 12 years, you need about 6 percent a year, and anything less means saving more along the way. The savings goal calculator finds the monthly deposit that closes a gap like that at a rate you choose.
Inflation and fees: the rule for halving
Anything that compounds against you follows the same rule, in the other direction. At 3 percent inflation prices double in about 24 years, which means the buying power of money left in a drawer halves in 24 years; at 2 percent it takes 36, at 5 percent about 14. The inflation calculator does this with the actual consumer price index between two dates instead of an assumed rate. A yearly fee works the same way on an investment: 1 percent a year, compounded, means that after roughly 72 years you end up with half of what the same money would have grown to without the fee, and after 36 years with about 70 percent of it.
Monthly compounding
Savings accounts usually compound monthly. At the same nominal rate that doubles the money slightly sooner, because interest starts earning interest within the year. At 6 percent yearly the exact doubling time is 11.9 years; compounded monthly it is 11.6. At 12 percent the two are 6.1 and 5.8 years. The rule of 72 sits between the two cases, which is one more reason it works as well as it does in practice.
Where it breaks
- Simple interest. If the interest is paid out and never reinvested, an amount doubles in exactly 100 ÷ rate years: 25 years at 4 percent, not 18. The rule of 72 only applies when growth compounds.
- Very high rates. Above 20 percent the rule understates the time by a growing margin. Use 69.3 ÷ rate + 0.35, or the exact formula.
- Changing rates. The rule assumes one rate for the whole period. Real returns vary year to year; the rule describes the average compound rate, which is what CAGR measures.
- Taxes and fees. Doubling time depends on the rate you keep. A 7 percent return taxed down to 5 percent doubles in about 14 years, not 10.
Frequently asked questions
What is the rule of 72?
Divide 72 by a yearly growth rate in percent and you get roughly the number of years it takes for an amount to double. At 6 percent, 72 ÷ 6 = 12 years; at 9 percent, 8 years. The exact time at 6 percent is 11.9 years, so the rule is a close shortcut for ordinary interest, investment and inflation rates.
Why 72 and not 70 or 69.3?
The exact constant comes from the natural logarithm of 2, which is 0.693, so a rule of 69.3 is the mathematically clean version for continuous compounding. For yearly compounding the right constant drifts upward with the rate: about 70 at 2 percent, 72 at 8 percent, 76 at 20 percent. 72 is picked because it sits in the range of typical rates and divides evenly by 2, 3, 4, 6, 8, 9 and 12, which makes the arithmetic easy in your head.
Does the rule of 72 work for inflation?
Yes, in reverse. At 3 percent inflation prices double, and the buying power of cash halves, in about 72 ÷ 3 = 24 years. The exact figure is 23.4 years. The same goes for any yearly cost that compounds, such as a fund fee: a 1 percent fee halves what a dollar would otherwise have grown to over roughly 72 years.
How do I find the rate I need to double my money in a set time?
Turn the rule around: rate ≈ 72 ÷ years. To double in 10 years you need about 7.2 percent a year; the exact answer is 7.18 percent. To double in 6 years you need about 12 percent, exactly 12.25.
When does the rule of 72 stop being accurate?
At high rates and for anything that does not compound. At 36 percent the rule says 2 years, the exact answer is 2.25, an error of three months. Simple interest, where the interest itself earns nothing, doubles an amount in exactly 100 ÷ rate years, so the rule of 72 understates that time by almost a third. For a rate below 1 percent or above about 25 percent, use the exact formula or a calculator.