Rule of 72 Calculator

The Rule of 72 is a linear approximation of a logarithmic relationship, so it is most accurate for interest rates roughly in the 6% to 10% range and drifts further from the exact figure the further the rate moves outside that band. At low rates the rule overestimates the true doubling time (at 1%, the rule says 72 years against an exact 69.7), and at high rates it underestimates it (at 50%, the rule says 1.44 years against an exact 1.71) -- the two cross at around 7.85%. The Exact Years figure, computed directly from logarithms, is always the more precise number if you need it.

No -- Starting Amount has no effect on Years to Double or Exact Years to Double at all. Doubling time under compound interest depends purely on the rate of return, not on the dollar amount invested: $1,000 growing at 8% doubles in the same amount of time as $1,000,000 growing at 8%. Starting Amount only determines the dollar value shown in Doubled Amount, Tripled Amount, and the growth chart.

The relationship is inverse and roughly linear in 1/rate -- doubling the interest rate roughly halves the time to double your money. The Rule of 72 estimate (72/rate) is exactly inversely proportional, but the true exact-math relationship is a touch worse than half: money growing at 4% takes about 17.7 years to double (exact), while money at 8% takes about 9.0 years, not the 8.8 you'd get from a clean halving, because the underlying logarithm grows slightly slower than the rate itself. The effect is small at typical rates but compounds at higher ones -- 16% takes about 4.7 years, still a touch more than half of the 8% figure.

It doesn't -- quadrupling is mathematically identical to doubling twice, since compounding is multiplicative: doubling once and then doubling again multiplies your money by 2 times 2, which is 4. Years to Quadruple is computed directly using log(4), and it always comes out to almost exactly twice Years to Double at the same rate, confirming that two consecutive doublings and one quadrupling take the same total time.