The Rule of 72 is one of the most useful mental maths shortcuts in personal finance. It lets you estimate how long it takes for an investment to double in value — without a calculator.
What Is the Rule of 72?
Divide 72 by your annual interest rate, and the result is approximately the number of years it takes your money to double.
Years to double ≈ 72 ÷ Annual interest rate (%)
Example: At a 6% annual return, your investment doubles in approximately 72 ÷ 6 = 12 years.
Why 72?
The mathematically precise formula for doubling time uses natural logarithms:
Years to double = ln(2) / ln(1 + r)
Where r is the interest rate as a decimal. For small rates, this simplifies to approximately 0.693 / r. Multiplied out, that's 69.3 / rate (%).
So why 72 instead of 69.3? Because 72 has more factors (1, 2, 3, 4, 6, 8, 9, 12), making mental arithmetic much easier. And for typical interest rates (6–10%), 72 gives a more accurate result than 69 anyway.
The Rule of 72 at Common Interest Rates
| Interest Rate | Years to Double (Rule of 72) | Exact Years |
|---|---|---|
| 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 |
| 15% | 4.8 years | 4.96 years |
| 18% | 4 years | 4.19 years |
The rule is most accurate between 6% and 10% — precisely the range of typical long-term investment returns.
Reverse Application: Finding the Rate
You can also use the Rule of 72 in reverse: if you know the time horizon, find the rate needed to double your money.
Required rate ≈ 72 ÷ Years you have
Example: You want to double your money in 9 years. You need a return of approximately 72 ÷ 9 = 8% per year.
Practical Applications
Long-Term Investing
If the stock market returns an average of 8% annually, a £10,000 investment doubles to £20,000 in about 9 years. After 18 years it's £40,000. After 27 years it's £80,000 — without adding another penny.
Inflation
The Rule of 72 applies to negative compounding too. At 3% inflation, prices double in 24 years. Something that costs £100 today will cost £200 in 2048.
Debt
Credit card debt at 18% interest doubles in 4 years if you make no payments. The rule makes the danger of high-interest debt viscerally clear.
Savings Accounts
A savings account paying 4% interest doubles your money in 18 years. Compare that to a 6% account — doubles in 12 years. That 6-year difference is enormous over a lifetime of saving.
Rule of 70 and Rule of 69.3
For more precision:
- Rule of 69.3 — Most mathematically accurate, but 69.3 is harder to divide mentally
- Rule of 70 — Good for rates that are multiples of 7 (7%, 14%)
- Rule of 72 — Best all-rounder, especially accurate at 6–10%
| Rate | Rule of 69.3 | Rule of 70 | Rule of 72 | Exact |
|---|---|---|---|---|
| 5% | 13.86 | 14.0 | 14.4 | 14.21 |
| 8% | 8.66 | 8.75 | 9.0 | 9.01 |
| 10% | 6.93 | 7.0 | 7.2 | 7.27 |
For most practical purposes, the Rule of 72 is accurate enough.
The Power of Small Rate Differences
The Rule of 72 makes it easy to see how much rate differences matter:
| Rate | Doubles in | £10,000 after 36 years |
|---|---|---|
| 4% | 18 years | £40,000 (2 doublings) |
| 6% | 12 years | £80,000 (3 doublings) |
| 8% | 9 years | £160,000 (4 doublings) |
| 9% | 8 years | £320,000 (4.5 doublings) |
A 2% difference in rate leads to dramatically different outcomes over decades. This is why investment fees matter so much — a 1% annual fee might sound small, but it effectively steals years of doubling time.
Compound Frequencies
The Rule of 72 assumes annual compounding. For more frequent compounding:
- Monthly compounding: Use 72 as normal — the difference is small
- Continuous compounding: Use 69.3 instead of 72
Common Misconceptions
"The rule only applies to investments" — It applies to anything that grows exponentially: inflation, debt, population, bacteria, website traffic.
"72 is arbitrary" — It's chosen because it divides evenly by 1, 2, 3, 4, 6, 8, 9, 12, and 18, covering the most useful interest rates.
"More precise calculators make it obsolete" — The rule's value is speed. During a conversation, a meeting, or a quick back-of-envelope calculation, the Rule of 72 beats pulling out a calculator.
Quick Reference
Years to double = 72 ÷ rate
Rate needed = 72 ÷ years
Doublings in N years = N ÷ (72 ÷ rate)