The Rule of 72, explained
A quick mental shortcut for estimating how long money takes to double.
The Rule of 72 is the fastest mental-math trick in personal finance: divide 72 by an annual compounding rate, and you get roughly how many years it takes for money to double. No calculator, no formula to remember — just one division. It’s remarkably close to correct across the rates that actually matter for savers, which is why it’s survived as a shortcut for centuries.
The shortcut, and why it works
Doubling time at a compounding rate r is exactly ln(2) / ln(1 + r)— correct, but not something anyone works out in their head. The Rule of 72 is an approximation of that formula that happens to simplify to a clean constant (72, rather than the mathematically “purer” 69.3 from a continuous-compounding version) because 72 divides evenly by so many common rates — 6, 8, 9, 12 — making the mental division actually easy to do without a calculator.
- At 12% (a common assumed long-run equity return): 72 ÷ 12 = 6 years to double.
- At 8% (a typical fixed-deposit-ish rate): 72 ÷ 8 = 9 years to double.
- At 7.1% (PPF’s current guaranteed rate): 72 ÷ 7.1 ≈ 10.1 years to double.
₹1,00,000 compounding at 12% a year for exactly 6 years — the Rule of 72’s estimate — grows to ₹1,97,382 using the real compound-interest formula. That’s within a couple of percent of doubling, from a shortcut that took one division to produce.
How accurate it actually is
| Rate | Rule of 72 estimate | Actual doubling time | Gap |
|---|---|---|---|
| 7.1% | 10.14 years | 10.11 years | 0.03 years |
| 8% | 9.00 years | 9.01 years | 0.01 years |
| 12% | 6.00 years | 6.12 years | 0.12 years |
| 24% | 3.00 years | 3.22 years | 0.22 years |
The pattern is consistent: the rule is nearly exact in the 6–10% band most real savings and debt instruments actually sit in, and drifts further off the higher the rate climbs. It’s a mental shortcut for a quick sanity check, not a substitute for running the real numbers when a decision actually depends on the precise year.
See how compounding grows a deposit at different rates and frequencies.
Why it breaks for simple interest
The Rule of 72 assumes compounding— each year’s interest earning further interest. Simple interest never does that: it adds the same flat rupee amount every year, so the actual formula for doubling time is different (and much simpler) — 100 / rate, not 72 / rate.
At 8%, compounding doubles your money in about 9 years (matching the Rule of 72’s estimate almost exactly). The same 8% under simple interest takes 12.5 yearsto double — over 3 years longer, because none of the interest already paid out is itself earning anything. Applying the Rule of 72 to a simple-interest instrument overstates how fast it grows.
This is worth checking before you use the shortcut: most market-linked and bank-declared rates (mutual funds, PPF, EPF, recurring compound instruments) genuinely compound, so the Rule of 72 applies directly. A handful of simple-interest products — some short-term loans, a few older deposit schemes — don’t, and the rule will make them look like they double faster than they really do.
See how compounding grows a deposit at different rates and frequencies.
Work out interest on a non-compounding loan or deposit quickly.
All figures are indicative and for educational purposes only — not financial advice.
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