Rule of 72 (Investment Doubling)

The Rule of 72 and exact doubling time

The Rule of 72 tells you roughly how long an investment needs to double at a constant compound rate. You just compute t ≈ 72 / r%. At 8% per year, money doubles in about 9 years; bump that to 12% and you're looking at 6 years. If you want the exact figure, the formula is t = ln 2 / ln(1 + r), which works out to 9.006 and 6.116 years for those two rates. Between 5% and 15% the shortcut stays within about 1% of the truth, and that band covers where most retail investments sit.

So why 72 instead of 70 or 69? The number divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which is exactly what you want for arithmetic in your head. It also sits comfortably between two more precise values: 69.3 (which is ln 2 · 100) and 70 (the one used for continuous compounding). When rates drop below 4%, switch to 70. Above 20%, the rule starts overstating the time and you can't trust it anymore.

Practical reference points

With Brazil's Selic hovering around 15% per year, Tesouro Selic doubles in roughly 4.8 years gross, or 5.6 once you take out 15% income tax. The S&P 500 has returned about 7% in real terms over the long run, which doubles your purchasing power every decade. On the other side, 4% inflation quietly cuts the value of cash in half every 18 years. The rule is handy as a reality check too. Take those "double your money in 30 days" pitches: hitting that needs roughly 2.4% a month, and compounded over a year that's 33%, which fixed income only reaches with extreme risk.

FAQ

Does the rule work for monthly rates? It does, as long as the rate is in the same time unit. A rate of 1% per month doubles your money in roughly 72 months, so 6 years, and the answer is off by less than half a month.

What about triple-your-money time? There's a sibling for that, the Rule of 114: t ≈ 114 / r%. Want a tenfold return? Then it's 231 / r%.

Why is my real doubling time longer than the rule suggests? The math assumes a steady compounded rate where gains get reinvested after fees and taxes come out. In Brazil that means accounting for the regressive income tax, which runs from 22.5% down to 15%, plus custody fees, before you plug a number into the rule.