An original TeaLamp explainer based on the sources listed below. Prepared by the TeaLamp Editorial Team with the help of AI.
The rule of 72 is one of the oldest and handiest shortcuts in money: divide 72 by a yearly interest rate and you get roughly how many years it takes for money to double. It needs no calculator, it works for savings, debts and prices alike, and it turns the slippery idea of compound interest into something you can picture in a few seconds.
Key takeaways on the rule of 72
- Divide 72 by the annual rate (as a plain number, so 6 for 6%) to estimate the years needed for something to double.
- The shortcut is close to exact for rates between about 3% and 12%, and drifts a little outside that range.
- It works in both directions: it shows how fast savings grow, how fast debt grows and how fast inflation halves what cash can buy.
- Small differences in rates or fees look tiny as percentages but become large when you turn them into doubling times.
- It is an estimate that assumes a steady rate, with nothing added or taken out. Real returns go up and down.
Compound interest in one minute
Simple interest pays you only on the money you first put in. Compound interest pays you on that money and on the interest it has already earned. The US Securities and Exchange Commission’s investor site defines it in exactly those terms: interest paid on principal and on accumulated interest.
That second part is what makes the growth speed up. Put $1,000 away at 6% a year and you earn $60 in the first year. In the second year you earn 6% on $1,060, which is $63.60. The extra $3.60 looks like nothing, but it keeps building on itself. After 12 years the pile has roughly doubled, and after 24 years it has roughly doubled again, to about $4,000. Growth that feels slow at the start becomes steep later, which is why people say that time matters more than timing.
Where the number 72 comes from
The rule is old. Historians of finance point to the Summa de arithmetica, a mathematics textbook by the Italian friar Luca Pacioli printed in Venice in 1494. In a passage on interest, Pacioli tells readers to keep 72 in mind and divide it by the rate to find the years for capital to double, giving 6% and 12 years as his example. He did not explain why it works, which suggests merchants were already using it before him. The same book is famous for its early account of double-entry bookkeeping, so the rule of 72 has been sitting next to the foundations of modern accounting for more than five centuries.
The mathematical reason is neat. The exact doubling time is the natural logarithm of 2 (about 0.693) divided by the natural logarithm of one plus the rate. For small rates, that comes out close to 69.3 divided by the rate. So why 72 and not 69? Partly because 72 is friendlier for mental arithmetic: it divides cleanly by 2, 3, 4, 6, 8, 9 and 12. And partly because, at the everyday rates people actually meet, a slightly bigger number makes up for the way the simple formula undershoots.
Merchants used quick rules for interest long before calculators. Image generated by AI.
How accurate is the rule of 72?
We worked out the exact doubling times for a range of yearly rates, compounded once a year, and set them beside the shortcut. The table shows how close the guess lands.
| Yearly rate | Rule of 72 estimate | Exact doubling time |
|---|---|---|
| 2% | 36 years | 35.0 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 |
| 18% | 4 years | 4.2 years |
| 24% | 3 years | 3.2 years |
Between about 4% and 12% the rule is off by a few months at most. At very low rates it slightly overstates the wait, and at high rates it slightly understates it. Some people use 70 for low rates, or 69 for interest that compounds continuously, but for a quick sense of scale 72 does the job.
Using the rule of 72 on savings
The real power of the shortcut is that it turns percentages into years, and years are easier to feel. A savings account paying 1% doubles your money in about 72 years, which is most of a lifetime. One paying 4% does it in about 18. Those two rates sound only three points apart, yet one doubles your money roughly four times faster.
Time does the rest. Money that grows at 6% doubles about every 12 years, so over 36 years it doubles three times and ends up around eight times larger. Start 12 years later and you lose one whole doubling, so you finish with half as much, even if every other choice is the same. That is the quiet case for starting early with small amounts, rather than waiting until you can save a lot. If you want to test your own numbers, the SEC’s free compound interest calculator lets you change the starting sum, monthly additions, rate and years.
Fees work the same way, only backwards
A yearly fee is a rate too, and it eats into growth just as steadily. If an investment earns 7% before costs and charges 1% a year, the money grows at roughly 6%. By the rule of 72, that stretches the doubling time from about 10.3 years to 12. Over a working life of four decades, that is the difference between about four doublings and a little over three. A fee that looks small on a statement can quietly cost a large share of the final total.
Time works for savers and against unpaid high-rate debt. Image generated by AI.
Using it on debt
The rule is just as useful as a warning light. Interest on unpaid debt compounds too. The US Federal Reserve’s consumer credit figures put the average interest rate on credit card accounts at around 21% a year in 2026. Divide 72 by 21 and you get a little under three and a half years. In other words, a balance that is left to grow at that rate, with no payments and no new charges, roughly doubles in about three and a half years.
Seen that way, paying down a high-rate card is one of the surest “returns” available, because every dollar repaid stops a dollar from doubling against you. It also explains why the order of payments matters: clearing the highest rate first slows the fastest-growing part of the debt.
Using it on inflation
Run the rule on rising prices and it tells you how fast cash loses buying power. At 2% inflation, the rate many central banks, including the Federal Reserve, aim for over the long run, prices double in about 36 years. At 3%, they double in about 24. So money kept in a drawer for 24 years at 3% inflation buys roughly half of what it once did. That is why savers look at the “real” rate, the interest rate minus inflation. An account paying 4% while prices rise 3% grows your buying power by only about 1% a year, which by the rule of 72 means doubling it in about 72 years.
Where the shortcut falls short
The rule of 72 is a thinking tool, not a forecast. It assumes the same rate every year, no money added or withdrawn and no taxes along the way. Real investments rise and fall, sometimes sharply, and past returns do not promise future ones. Debts can carry fees, changing rates and minimum payments that the rule ignores. Used honestly, it is best for comparing options side by side: this rate against that one, this fee against that one, saving now against saving later.
Why it matters: most money decisions are made with percentages, and percentages hide how much time changes things. The rule of 72 translates them into years, a unit everyone understands. It makes the benefit of starting early easier to see, the cost of high-interest debt harder to ignore and the slow drain of inflation and fees visible. This article is general education, not personal financial advice; for decisions about your own money, a qualified, independent adviser can look at your full picture.
Related reading
For another look at the numbers behind money and work, see our explainer on how long new businesses usually last.
Frequently asked questions
Does the rule of 72 work for monthly compounding?
Yes, roughly. More frequent compounding makes money grow a little faster, so the true doubling time is slightly shorter than the estimate. For everyday rates the difference is only a few months.
Why not use 70 instead of 72?
Both are approximations. Seventy is a little closer at low rates and for continuous growth, while 72 is easier to divide in your head and fits common rates of about 6% to 10% very well.
Can I use it backwards to find a rate?
Yes. If you want money to double in 9 years, divide 72 by 9: you would need about 8% a year.
Sources
- Investor.gov (US SEC): Compound interest glossary entry
- Investor.gov (US SEC): Compound interest calculator
- Virginia State Corporation Commission: The basics of saving and investing (Rule of 72 worksheet, PDF)
- MacTutor History of Mathematics: Pacioli’s rule of 72 in the Summa de arithmetica (1494)
- British Actuarial Journal: The emergence of compound interest
- Federal Reserve: Consumer Credit G.19 (credit card interest rates)
- Federal Reserve: Why does the Federal Reserve aim for inflation of 2 percent over the longer run?
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