What Is the Rule of 72?
The Rule of 72 is a simple mathematical shortcut for estimating how long it takes an investment to double in value at a fixed annual rate of return. Divide 72 by the annual interest rate (expressed as a whole number), and the result is the approximate number of years to double your money.
It requires no calculator, no spreadsheet, and no finance degree. Yet it gives results surprisingly close to the exact answer for rates in the range most investors and savers encounter. The rule dates back at least to Luca Pacioli's 1494 mathematical text and remains one of the most practical tools in personal finance.
The Formula
72 = the constant (works best for rates 2%–15%)
Annual Rate = percentage, not decimal (use 8, not 0.08)
The rule also works in reverse: if you know how many years you want to double your money in, divide 72 by that number of years to find the required annual return. Want to double in 9 years? You need roughly 72 ÷ 9 = 8% per year.
Worked Examples at Various Rates
A high-yield savings account earns 4% APY. How long until your balance doubles?
Exact answer using the compound interest formula: 17.67 years. The Rule of 72 is off by only 0.33 years — well within any practical planning range.
A diversified index fund averages 8% annual returns. How often does the portfolio double?
Invest $10,000 at age 25 and let it grow: $20,000 by 34, $40,000 by 43, $80,000 by 52, and $160,000 by 61. No additional contributions required.
A credit card charges 24% APR. If you make no payments, how long until the balance doubles?
A $5,000 balance becomes $10,000 in just three years. This is why high-interest debt must be treated as a financial emergency — the same compounding that builds wealth works with devastating speed against borrowers.
Rates vs. Doubling Times
| Annual Rate | Rule of 72 (years) | Exact Answer (years) | Error | Common Context |
|---|---|---|---|---|
| 2% | 36.0 | 35.0 | +1.0 | Savings account, CDs |
| 4% | 18.0 | 17.7 | +0.3 | High-yield savings, bonds |
| 6% | 12.0 | 11.9 | +0.1 | Conservative portfolio |
| 8% | 9.0 | 9.0 | 0.0 | Broad market index |
| 10% | 7.2 | 7.3 | −0.1 | Aggressive equities |
| 12% | 6.0 | 6.1 | −0.1 | High-growth stocks |
| 24% | 3.0 | 3.2 | −0.2 | Credit card debt |
The Rule of 72 is most accurate around 8%, which happens to be close to long-run stock market returns. It slightly overestimates doubling time at lower rates and slightly underestimates it at higher rates, but the error is never large enough to matter for planning purposes within the 2%–15% range.
When the Rule Breaks Down
At very high interest rates — above 20–25% — the Rule of 72 starts to produce meaningfully inaccurate results. For precise work at extreme rates, use the Rule of 69.3 instead, which is derived from the natural logarithm:
ln = natural logarithm
69.3 = more mathematically precise constant
72 = easier to divide mentally, nearly as accurate for typical rates
72 was chosen over 69.3 for one simple reason: it has more integer divisors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72), making mental arithmetic cleaner. At the rates most savers and investors encounter, the difference is negligible.
The rule also assumes compound interest and a constant rate. For simple interest loans, or assets with highly variable returns, the approximation is less applicable — though it still provides a useful ballpark.
The Rule of 115: Tripling Time
Need to estimate how long it takes for money to triple? Use the same logic with a different constant: divide 115 by the annual rate.
~14.4 years
At 6%: 115 ÷ 6 = ~19.2 years
Similarly, dividing 144 by the rate gives a rough estimate for quadrupling time. These extended rules are less commonly used, but they illustrate how the same mental math framework scales to other growth multiples.
Using It for Inflation
The Rule of 72 is equally useful for understanding the corrosive effect of inflation. Divide 72 by the inflation rate to find how many years it takes for prices to double — or equivalently, for the purchasing power of your cash to be cut in half.
- At 3% inflation: 72 ÷ 3 = 24 years to halve purchasing power
- At 4% inflation: 72 ÷ 4 = 18 years to halve purchasing power
- At 7% inflation (as seen in 2022): 72 ÷ 7 = roughly 10 years to halve purchasing power
This is why holding large amounts of cash long-term is a losing strategy. Inflation silently erodes the real value of every dollar sitting idle. A dollar in a savings account earning 1% during a 4% inflation period loses purchasing power every single year. For more on this topic, see our full guide on how inflation erodes your savings.
The Rule of 72 for Debt
Debt compounds against you just as powerfully as investments compound for you.
If you carry a balance on a credit card at 20% APR and make only minimum payments that barely cover the interest, the outstanding balance effectively doubles every 3.6 years. A $3,000 balance could become $6,000 in less than four years, $12,000 in less than eight.
This framing can change how urgently you treat high-interest debt. It is not just a monthly expense — it is an investment in reverse, compounding at 15–30% per year against your net worth. Eliminating that debt is equivalent to earning a guaranteed, tax-free return equal to the interest rate. For a complete framework on which debts to tackle first, read our article on how compound interest works.
See the Exact Numbers
The Rule of 72 gives you a fast estimate. Our calculators give you the precise figures with charts and year-by-year breakdowns.
Compound Interest Calculator → Investment Return Calculator →