Rule of 72 — Years to Double Your Money
The Rule of 72 is the fastest mental shortcut in finance: divide 72 by your annual rate of return (in percent) to estimate the number of years it takes an investment to double through compounding. No logarithms, no calculator — one division. At an illustrative 8%/year, money doubles in roughly 72 ÷ 8 = 9.0 years; the exact logarithmic answer is 9.0 years, off by less than a fortnight. That accuracy at everyday rates is why the rule has survived for centuries.
The real value of the rule is intuition about rates. Doubling your return does not double your ending balance — it halves the time to double: at 6%/year money doubles in 12.0 years, but at 12%/year it doubles in just 6.0 years. A couple of percentage points that look trivial on paper compound into a very different outcome over a working lifetime, which is precisely why fees and rate differences matter so much for long-horizon investors.
Drag the expected-return slider in the tool above to read the doubling time instantly. A caveat applies to everything here: every rate on this page is an illustrative assumption, not a quote. Real returns on deposits, bonds and funds vary by date and by risk, so plug in your own number. The Rule of 72 also approximates compound growth only — it does not apply if you spend the interest each period (simple interest).
Where the Rule of 72 comes from and how the tool computes it
The formula
The widget performs a single calculation:
Y = 72 / r
| Symbol | Meaning |
|---|---|
| Y | Approximate number of years for the money to double |
| r | Annual rate of return, expressed in percent per year |
Example: at r = 8, Y = 72 ÷ 8 = 9.0 years. You can run it in reverse, too: to double inside 6 years you need about 72 ÷ 6 = 12.0%/year.
Why 72 and not some other number?
The exact doubling time is ln(2) / ln(1 + r), where ln is the natural logarithm. A first-order expansion puts the numerator at ln(2) × 100 ≈ 69.3. People round 69.3 up to 72 because 72 divides evenly by many small numbers (2, 3, 4, 6, 8, 9, 12), making the mental arithmetic painless, and because at the common 6–10%/year band 72 actually tracks the true value better than 69.3 does. At r = 8%, the exact formula returns 9.01 years while the Rule of 72 gives 9.0 years.
When is the rule accurate?
- Most accurate around 6–10%/year — conveniently the band where long-run portfolio return assumptions usually sit.
- Drifts at the extremes. For very low rates (1–2%) use 69 or 70 instead; for very high rates (above ~20%) the approximation widens.
- Compounding only. If interest is withdrawn and spent each period (simple interest), money does not double on this schedule.
What it ignores
The rule assumes a constant rate for the whole period and ignores taxes, fees and inflation. It answers "how long to double in nominal terms", not "how long to double purchasing power". For an exact future value use the compound interest tool; to back out a growth rate from a known start and end value, use the CAGR calculator.
Worked example: doubling time across rates
Illustrative assumptions: compound growth, a constant rate for the whole period, no taxes, fees or inflation. The last column shows the exact doubling time (ln 2 ÷ ln(1+r)) so you can see the rule's error.
| Rate (%/year) | Rule of 72 (72 ÷ r) | Exact years | Difference |
|---|---|---|---|
| 3% | 24.0 years | 23.45 years | 0.55 years |
| 6% | 12.0 years | 11.90 years | 0.10 years |
| 8% | 9.0 years | 9.01 years | -0.01 years |
| 10% | 7.2 years | 7.27 years | -0.07 years |
| 12% | 6.0 years | 6.12 years | -0.12 years |
| 15% | 4.8 years | 4.96 years | -0.16 years |
Read the 8% row (the tool's default): 72 ÷ 8 = 9.0 years, almost identical to the exact 9.01 years. Read down the column and the "double the rate, halve the time" pattern jumps out: going from 6% (12.0 years) to 12% (6.0 years) cuts the doubling time exactly in half.
Using it in reverse: what rate doubles money in X years?
Flip the formula to r = 72 / Y. To turn 200 million VND into 400 million VND in 6 years you would need roughly 72 ÷ 6 = 12.0%/year — a high return that carries far more risk than a bank deposit. This reverse check is a quick reality test for return promises: anyone pitching "double your money in 2 years" is implying about 36%/year, a number that should make you cautious.
Frequently asked questions
What is the Rule of 72?
The Rule of 72 is a mental shortcut for estimating how many years it takes money to double through compounding: divide 72 by the annual rate in percent. For example, at an illustrative 8%/year, 72 ÷ 8 ≈ 9.0 years. It is an approximation you can do in your head without a calculator.
How do I calculate the Rule of 72?
Use Y = 72 / r, where Y is the years to double and r is the annual rate in percent. Check: r = 8 gives Y = 72 ÷ 8 = 9.0 years. In reverse, r = 72 / Y — so doubling within 6 years needs about 12.0%/year.
How accurate is the Rule of 72?
Quite accurate between roughly 6% and 10%/year. At 8%/year the rule gives 9.0 years versus the exact answer ln(2)/ln(1.08) = 9.01 years — an error of under two weeks. The gap widens at very low rates (below ~2%) or very high rates (above ~20%).
Why is the number 72 used?
The exact doubling time rests on ln(2) ≈ 0.693, giving an approximate numerator of 69.3. People round up to 72 because it divides evenly by many small numbers (2, 3, 4, 6, 8, 9, 12), making mental arithmetic easy, and because at common 6–10%/year rates 72 tracks the true value even better than 69.3. For very low rates, use 69 or 70 instead.
What return do I need to double my money in 6 years?
Flip the formula: r = 72 / Y = 72 ÷ 6 = 12.0%/year. That is a high return that usually carries far more risk than a bank deposit. Anyone promising to "double your money in 2 years" is implying about 36%/year — a figure that should prompt skepticism.
Does the Rule of 72 work for savings accounts or only investments?
It works for both, as long as growth is compound — meaning interest is reinvested rather than spent. For a term deposit, that means choosing to roll over principal plus interest at maturity. The rule answers "how long to double in nominal terms" and ignores taxes, fees and inflation; for an exact future value, use FiMo's compound interest tool.