Finance · 5 min read
How to Use the Rule of 72
Years to double ≈ 72 ÷ rate% — next to the exact compound formula
The Rule of 72 estimates how long a balance takes to double at a constant annual rate: divide 72 by the rate in percent. This tutorial walks through that shortcut, the exact doubling time ln(2)/ln(1 + r), an 8% worked example, and a playground that plots the rule against the exact formula as you move the rate. Figures are illustrative; fees and taxes are omitted.
Written by the My Calculator Stack editorial team. About our methods
These figures are illustrative. Fees, taxes, and product-specific rules are omitted. This is not investment, tax, or financial advice.
1.What the Rule of 72 is
The Rule of 72 is a mental-math shortcut for doubling time under annual compounding at a constant rate. At 8%, 72 ÷ 8 = 9 years. It is an approximation, not a quote, and it is most accurate for moderate positive rates (roughly 6% to 10%). It ignores fees, taxes, extra deposits, and rate changes.
2.The formulas
The rule is t ≈ 72 / r, where r is the annual rate in percent (8 means 8%, not 0.08). The exact doubling time from FV = PV(1 + r)^t with FV = 2·PV is t = ln(2) / ln(1 + r), now with r as a decimal (8% → 0.08). The two agree closely near 8%. At very low or high rates the gap widens — which is what the playground is for. The Rule of 72 calculator on this site reports the shortcut only.
\[ \begin{aligned}t &\approx \frac{72}{r_{\%}} \\t_{\mathrm{exact}} &= \frac{\ln 2}{\ln(1+r)}\end{aligned} \]
3.Worked example
Take an 8% annual rate — the same default as the Rule of 72 calculator. The shortcut gives 72 / 8 = 9 years. The exact compound formula is ln(2) / ln(1.08) ≈ 9.01 years. At 8% the rule is almost exact. At 1% the rule says 72 years while the exact time is about 69.7; at 18% the rule says 4 years while the exact time is about 4.19.
\[ t=\frac{72}{8}=9,\quad \frac{\ln 2}{\ln 1.08}\approx 9.01 \]
4.Shortcut versus exact doubling time
Move the annual rate to see the Rule of 72 marker travel next to the exact ln(2)/ln(1+r) marker. This is a teaching widget — constant annual compounding, no extra deposits, no fees, no full calculator chrome. Open the Rule of 72 calculator when you want the standalone shortcut.
Inline playground
Illustrative — fees and taxes omitted
Years to double
Rule 9.00 · exact 9.01
72 / 8 = 9 · ln(2)/ln(1.08) ≈ 9.01
Illustrative only — constant annual compounding, no extra deposits, no fees or taxes.
Open the full Rule of 72 calculator →5.Open the full calculator
The Rule of 72 calculator uses the same 72 ÷ rate% shortcut, the same 8% example, and the same limitation that taxes and fees are omitted. Browse other finance tools if you need future value, compound interest, or CAGR next.
Try it yourself
Open the related calculator and put these formulas to work.