Disclaimer: This article is for general informational purposes only and is not a substitute for professional financial or investment advice. Consult a SEBI-registered investment adviser before making any investment decisions.
The Rule of 72 is the oldest trick in personal finance: divide 72 by your annual return rate, and you get a reliable estimate of how many years it takes to double your money. No calculator needed. Useful in a meeting, on a napkin, or while reading a fund fact sheet.
But the rule is more than a parlour trick. Understanding where it comes from, where it is accurate, and where it misleads helps you use it correctly — and avoid the overconfidence that comes from applying any approximation outside its valid range.
The formula
Years to double ≈ 72 / Annual Rate (%)Equivalently, if you know how many years you have, you can find the required rate:
Required CAGR (%) ≈ 72 / Years to doubleThat is the complete formula. The elegance is in its simplicity: one division, an instant answer.
Where does 72 come from?
The mathematical root of the Rule of 72 is the doubling time formula for compound growth. If money grows at rate r annually, the exact time to double is:
t = ln(2) / ln(1 + r)Where ln is the natural logarithm. For small r, ln(1 + r) ≈ r, so:
t ≈ ln(2) / r ≈ 0.6931 / rExpressed as a percentage rate (so r = R/100):
t ≈ 69.3 / RThis is where the Rule of 69.3 comes from — and it is the exact answer for continuous compounding. For annual compounding (which is what most savings instruments use), the exact answer is slightly higher than the continuous-compounding estimate, and 72 provides a better approximation in that range.
More precisely: 72 happens to minimise the approximation error for rates between roughly 6% and 12% under annual compounding. Since this range covers most practical personal finance scenarios — PPF, FDs, equity mutual funds, index returns — the number 72 is pragmatically optimal, not arbitrary.
An additional reason 72 stuck: it has an unusually large number of integer divisors (2, 3, 4, 6, 8, 9, 12, 18, 24, 36). This means that for the most common return rates — 3%, 4%, 6%, 8%, 9%, and 12% — the division produces a whole number, making mental arithmetic effortless.
Accuracy range
The rule is accurate (within about 1–2%) for rates between approximately 6% and 15%.
| CAGR | Rule of 72 estimate | Exact doubling time | Error |
|---|---|---|---|
| 3% | 24.0 years | 23.4 years | +2.6% |
| 6% | 12.0 years | 11.9 years | +0.8% |
| 8% | 9.0 years | 9.0 years | ~0% |
| 10% | 7.2 years | 7.3 years | −1.4% |
| 12% | 6.0 years | 6.1 years | −1.6% |
| 15% | 4.8 years | 4.96 years | −3.2% |
| 25% | 2.88 years | 3.11 years | −7.4% |
| 50% | 1.44 years | 1.71 years | −15.8% |
The degradation at high rates is significant. At 50% CAGR the rule underestimates the doubling time by more than 15% — a meaningful error if you are making decisions based on it. At 6–12%, the error is under 2% and harmless for planning purposes.
The Rule of 69.3 for continuous compounding
If interest compounds continuously (which is a mathematical model used in bond pricing and some financial derivatives), the exact formula is:
Years to double = 69.3 / Annual Rate (%)For continuous compounding at 10%: 69.3 / 10 = 6.93 years. The exact answer is exactly 6.93 years — zero error.
For practical personal finance — savings accounts, mutual funds, PPF, FDs — compounding is annual, quarterly, or monthly, not continuous. In these cases, the Rule of 72 gives a slightly better approximation than 69.3 because it compensates for the rounding inherent in discrete compounding. Use the Rule of 69.3 only if you are working with continuously compounded rates.
Real examples with Indian instruments
PPF at 7.1%
The Public Provident Fund currently offers 7.1% per annum.
Years to double = 72 / 7.1 ≈ 10.1 yearsExact answer: 10.24 years. The rule is off by less than two weeks on a ten-year horizon — negligibly precise.
Practical implication: if you open a PPF account and contribute the maximum ₹1.5 lakh per year starting today, the accumulated corpus approximately doubles on an inflation-adjusted sense every decade. The standard PPF tenure is 15 years with extension options in 5-year blocks — about 1.5 doublings at the current rate.
Equity at 12% CAGR
Indian equity mutual funds have historically delivered approximately 12% CAGR over rolling 15–20 year periods.
Years to double = 72 / 12 = 6 yearsAt 12% CAGR, money doubles every 6 years. Over a 30-year investment horizon (a career), money doubles approximately 5 times: ₹1 lakh → ₹2 lakh → ₹4 lakh → ₹8 lakh → ₹16 lakh → ₹32 lakh. The Rule of 72 makes this compounding ladder immediately graspable.
You can verify any of these calculations using the Stock CAGR Calculator — enter your starting and ending values and years to confirm the effective CAGR, then apply the Rule of 72 to project further doublings.
Bank FD at 6.5%
A typical bank FD for a 5-year tenure might offer 6.5% per annum (rates vary).
Years to double = 72 / 6.5 ≈ 11.1 yearsIt takes more than 11 years to double your money in a bank FD at 6.5%. For context, the same money in equity at 12% CAGR would double in 6 years — reaching 4× the FD starting value in the same 11-year window.
This is not an argument against FDs (they serve specific purposes: capital safety, liquidity, predictability). It is an argument for understanding the compounding opportunity cost when comparing asset classes.
Inflation at 6%: the other side of doubling
The Rule of 72 is just as useful for understanding purchasing power erosion as it is for understanding growth. Inflation works exactly the same way — it compounds against you.
Years for purchasing power to halve = 72 / Inflation rate (%)At 6% average inflation:
72 / 6 = 12 yearsEverything that costs ₹100 today will cost approximately ₹200 in 12 years. Your savings — even at a 6% FD rate — are barely keeping pace with this erosion, because returns above 6% FD after tax may be minimal.
At 7% inflation (which is not unusual during commodity or food price spikes):
72 / 7 ≈ 10.3 yearsPurchasing power halves in about a decade. This is why financial planners insist that purely debt-based portfolios struggle to preserve real wealth over 20–30 year retirement horizons.
Using the Rule of 72 in reverse: finding the required CAGR
The rule works equally well in reverse. You know your doubling target and timeline — find the required rate:
Required CAGR (%) ≈ 72 / Years to doubleExample 1: Retirement planning You are 35 and want your ₹20 lakh corpus to become ₹80 lakh by age 55 — two doublings in 20 years.
- First doubling: 20 lakh → 40 lakh in 10 years
- Required CAGR for each doubling: 72 / 10 = 7.2%
At 7.2% CAGR, you get two doublings in 20 years. If your target is higher growth, the required CAGR scales accordingly.
Example 2: Child education fund You need ₹30 lakh in 9 years for a child’s higher education and currently have ₹15 lakh.
Required CAGR ≈ 72 / 9 = 8% per yearYou need an investment compounding at approximately 8% per annum. A diversified equity fund, a balanced advantage fund, or a combination of instruments targeting 8%+ CAGR would meet this goal. The Stock CAGR Calculator can verify: enter 15 lakh start, 30 lakh end, 9 years → 8.0% CAGR confirmed.
Example 3: Lump-sum investment goal A business owner has ₹50 lakh and wants it to become ₹1 crore in 5 years.
Required CAGR ≈ 72 / 5 = 14.4%This is an ambitious rate — achievable in a strong equity market environment, but not guaranteed. The rule immediately contextualises the risk level required: 14.4% CAGR is above typical large-cap fund returns and implies meaningful equity allocation with associated volatility.
Common pitfalls
Applying it to very high rates: At 100% CAGR (doubling every year), the rule gives 72/100 = 0.72 years. The exact answer for annual compounding is exactly 1 year. The rule fails badly here — never use it for CAGR above 25%.
Treating it as a guarantee: The Rule of 72 models deterministic compounding. Real investments are volatile. A fund that averages 12% CAGR over 20 years will have some years at +40% and others at −30%. The money does not double smoothly in exactly 6 years — it takes a volatile path that might temporarily show far more or far less than the expected amount at any given point. The rule describes the destination, not the journey.
Ignoring taxes: The doubling time the rule gives assumes you keep the full return. In practice, equity long-term capital gains above ₹1 lakh are taxed at 12.5% in India; debt fund gains are taxed at slab rate. After-tax CAGR is lower, and the effective doubling time is longer. Adjust the CAGR downward for after-tax estimates.
Using it for step-up SIPs or irregular contributions: The rule applies to a lump sum invested at a constant rate. If you are adding money every month (SIP) or drawing it down (retirement withdrawal), use a proper financial calculator or XIRR analysis.
A quick reference table
| Rate | Doubles every | Quadruples in |
|---|---|---|
| 4% (e.g. Post Office Savings) | 18.0 years | 36 years |
| 6% (e.g. FD) | 12.0 years | 24 years |
| 7.1% (PPF) | ~10.1 years | ~20.2 years |
| 8% (debt funds / gilt) | 9.0 years | 18 years |
| 10% (balanced funds) | 7.2 years | 14.4 years |
| 12% (large-cap equity) | 6.0 years | 12 years |
| 15% (mid-cap equity) | 4.8 years | 9.6 years |
| 18% (small-cap equity) | 4.0 years | 8.0 years |
The bottom line
The Rule of 72 is a mental model that makes compounding intuitive. It does not replace rigorous calculations — it complements them. Use it to instantly sense-check whether a return rate is plausible for a given goal, to explain investment growth to someone without a calculator, or to make inflation’s erosion of purchasing power tangible.
For precise numbers — when the stakes involve real investment decisions — use an exact CAGR calculation. The Rule of 72 is the shortcut; the formula is the source of truth.