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Rule of 72

fundamental concepts
Definition
A simple formula to estimate how long an investment will take to double in value: divide 72 by the annual return rate.

Explanation

At 8% annual return, money doubles in approximately 72/8 = 9 years. At 12%, it doubles in 6 years. At 4%, it takes 18 years. The Rule of 72 works because of the mathematics of compound interest: ln(2)/ln(1+r) ≈ 72/r for reasonable interest rates. It's a powerful tool for quick mental math and illustrates why small differences in return rates matter enormously over long periods. The difference between 7% and 10% annual return means doubling in 10.3 years versus 7.2 years — three extra years of waiting for each doubling.

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