Effortless Math › Personal Finance › The Rule of 72
The Rule of 72
The Rule of 72 is the most useful piece of mental arithmetic in personal finance. Divide 72 by the interest rate and you get, near enough, the number of years for money to double. It works for savings, for investments, and — the part people forget — for debt.
The rule
Three examples, in your head
Use the rate as a whole number, not a decimal. 6% is 6, not 0.06.
Seventy-two is chosen because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which covers most of the rates you meet. That convenience is the only reason it is 72 rather than 69 or 70.
Where 72 comes from
Doubling means the final amount is twice the principal, so in the compound interest formula you are solving 2 = (1 + r)t for t. Taking logarithms gives the exact answer:
ln(2) is about 0.693. For small rates, ln(1 + r) is close to r itself, so the expression is roughly 0.693 ÷ r — that is, 69.3 divided by the rate as a percentage. The rule rounds 69.3 up to 72 because the approximation drifts low as rates rise, and because 72 is far easier to divide. The two effects partly cancel.
How accurate it actually is
Close, over the range of rates that matter:
| Rate | Rule of 72 | Exact | Error |
|---|---|---|---|
| 2% | 36.0 yrs | 35.00 yrs | +1.00 yrs |
| 4% | 18.0 yrs | 17.67 yrs | +0.33 yrs |
| 6% | 12.0 yrs | 11.90 yrs | +0.10 yrs |
| 7% | 10.3 yrs | 10.24 yrs | +0.04 yrs |
| 8% | 9.0 yrs | 9.01 yrs | -0.01 yrs |
| 10% | 7.2 yrs | 7.27 yrs | -0.07 yrs |
| 12% | 6.0 yrs | 6.12 yrs | -0.12 yrs |
| 18% | 4.0 yrs | 4.19 yrs | -0.19 yrs |
| 24% | 3.0 yrs | 3.22 yrs | -0.22 yrs |
Between about 4% and 12% the rule is within a couple of months of the exact figure, which is far tighter than the precision of any assumption you are feeding it. At 2% it runs about half a year long, and by 24% it is overstating by more than four months on a three-year answer — proportionally much worse.
Running it backwards
The rule rearranges. If you know how long you have and you know what you need, it tells you the rate required:
Worked example
You have $8,000 and you want $16,000 in nine years. What return do you need?
This version is the more useful of the two, because it turns a vague goal into a testable number. If the answer comes back above about 10%, the goal needs more time or more money — not a better investment.
Using it on debt
The formula does not know whose money it is. A balance you are not paying doubles on exactly the same schedule.
| Debt | Typical rate | Doubles in |
|---|---|---|
| Federal student loan | 6.5% | 11 years |
| Car loan | 8% | 9 years |
| Credit card | 24% | 3 years |
| Payday loan | 390% APR | about 2 months |
Three years is the number to remember
An unpaid credit card balance at 24% doubles in about three years. A $2,000 balance ignored through college is roughly $4,000 at graduation and $8,000 three years after that. Nothing about the balance changed except time.
Where it stops working
- Very low or very high rates. Below about 3% or above about 15% the approximation drifts enough to matter. Use the logarithm.
- Rates that change. The rule assumes one constant rate. Real investment returns vary year to year, so the answer is an average-case estimate, not a schedule.
- Money you keep adding to. The rule describes a lump sum doubling. If you are contributing monthly, you need the future value of a series instead.
- Inflation. Doubling your dollars is not doubling your purchasing power. To work in real terms, subtract inflation from the rate first — 7% growth with 3% inflation is a 4% real rate, so the real doubling time is 18 years, not 10.
Practice, with answers
1. Your savings account pays 4%. How long until your money doubles?
Answer: About 18 years.
2. You have $3,000 and want $6,000 in six years. What annual return do you need?
Answer: About 12% — high enough that you should probably extend the timeline instead.
3. A $1,500 credit card balance sits at 24% APR and is never paid. Roughly what is it after nine years?
Answer: About $12,000.
4. Your investment returns 9% a year but inflation runs 3%. How long until your purchasing power doubles?
Answer: 12 years in real terms, not 8.
Check what you learned
Take the 10-question saving and compound interest quiz. It opens on the hub, and you will see your score, the correct answers, and explanations when you finish.
Keep going
- Compound interest, worked out — the exact formula this rule approximates
- Credit card minimum payment math — what the three-year doubling looks like month by month
- Personal finance glossary — APR, APY, principal, real rate
Questions people ask
Why is it 72 and not 69 or 70?
The mathematically exact constant is 69.3, from the natural logarithm of 2. Seventy-two is used instead because it divides evenly by 2, 3, 4, 6, 8, 9 and 12, which makes the mental arithmetic work for the rates people actually meet. The slight overstatement also offsets the approximation error, which runs in the other direction as rates rise.
How accurate is the Rule of 72?
Between about 4% and 12% it is usually within a couple of months of the exact answer. At 8% it says 9 years against an exact 9.01. Below 3% or above 15% it drifts enough that you should use the logarithm instead.
Can the Rule of 72 be used for debt?
Yes, and that is often the more useful direction. A credit card balance at 24% doubles in about three years if nothing is paid. A federal student loan at 6.5% doubles in about eleven.
Does the Rule of 72 work with monthly contributions?
No. It describes a single lump sum doubling at a fixed rate. If you are adding money every month you need the future value of a series formula, which is on the compound interest page.
How do I account for inflation?
Subtract the inflation rate from the return first, then apply the rule to what is left. A 9% return with 3% inflation is a 6% real rate, so purchasing power doubles in about 12 years rather than the 8 the nominal rate suggests.
Part of the Personal Finance hub — ten units, a free pacing guide, and worked examples with answers.