Rule of 72 Calculator
The rule of 72 is the mental shortcut investors use to price time: divide 72 by your annual return for the rough number of years needed to double the money. It takes one division, no calculator, and stays accurate for everyday decisions — until rates turn very low or very high and it starts to drift. This page gives that estimate, the exact logarithmic answer, and the rate needed to double in a chosen term.
Enter values
Results
- Years to double (rule of 72)
- 6
- Years to double (exact)
- 6.12
- Rate to double in 10 years
- 7.18%
How is the Rule of 72 calculated?
Enter your expected annual return, plus the number of years over which you would like an amount to double. The calculator divides 72 by the rate for the familiar estimate, solves the doubling equation exactly using natural logarithms for a second figure, then works backwards from your chosen years to report the annual rate that would really deliver a doubling. At 0% both doubling answers are undefined and appear as an em dash.
Formula
Estimate: years to double = 72 ÷ rate. Exact: t = ln(2) ÷ ln(1 + r), which solves (1 + r)^t = 2 with r as the annual rate in decimal form. In the other direction, doubling in T years requires r = (2^(1 ÷ T) − 1) × 100. The 72 stands in for 100 × ln(2) ≈ 69.3 because it divides cleanly by the rates people quote.
Example
At 12% a year, 72 ÷ 12 says your money doubles in 6 years; the exact equation gives 6.12 years, close enough for planning. Push the rate down to 1% and the rule claims 72 years while the exact answer is 69.66 — an overestimate of more than two years. Ask the reverse question instead: doubling in 10 years needs 7.18% a year.
Things to remember
Treat the rule as a conversation starter, not a forecast: markets rarely deliver a smooth 12% every year, and taxes on returns stretch the doubling time further. When the number carries weight — retirement targets, education funds — check it against the compound interest calculator before committing to a plan.
Frequently Asked Questions
Why does the rule of 72 use the number 72?
Because 72 divides neatly by 2, 3, 4, 6, 8, 9 and 12 — the rates people quote most often — and it sits close to 100 × ln(2) ≈ 69.3, the mathematically correct constant. The rounding keeps mental arithmetic easy while the error stays within a few percent.
How accurate is the rule of 72?
Between roughly 6% and 10% it lands within a rounding error of the exact answer: 8% doubles in 9 years by the rule and 9.01 exactly. Outside that band it drifts — at 1% the rule overstates the wait, and at 50% it understates it by over three months.
What is the rule of 72 used for with inflation?
Divide 72 by the inflation rate to find how long it takes prices to double and your cash to buy half as much. At 6% inflation that is 72 ÷ 6 = 12 years, which is why a stash under the mattress loses half its reach in a little over a decade.
Can I apply the rule of 72 to a SIP?
Only as a rough guide. The rule assumes one fixed annual rate compounded yearly, while a SIP invests monthly and market returns arrive unevenly. For a realistic corpus figure, run the SIP calculator with your monthly amount and expected return instead.
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