Calculate how long it takes to double your money at various interest rates using the Rule of 72, 69.3, and exact formulas.
The Rule of 72 estimates how many years an investment takes to double: divide 72 by the annual rate. This calculator returns that quick figure alongside the 69.3 rule and the exact doubling time computed from logarithms, side by side, so you can see how far the shortcut drifts. The surprise most people hit: the rule is not equally accurate at every rate. It is calibrated to be near-exact around 8%, but at 24% it understates the true doubling time by about 7%. Enter the rate as a whole number - 8, not 0.08.
A concrete input and expected output from the current implementation.
Input
8
Expected output
Rule of 72: 9.0 years. Rule of 69.3: 8.66 years. Exact (annual compounding): 9.01 years.
At 8% the three answers nearly converge because the Rule of 72 is calibrated to be near-exact around 6-8% for annual compounding: 72 / 8 = 9, while ln(2) / ln(1.08) = 9.006. The 69.3 figure matches the continuous-compounding value ln(2) / 0.08 = 8.66 years.
The calculator computes the shortcut 72 / r, the 69.3 rule, and the exact figure ln(2) / ln(1 + r), where r is the rate as a decimal. The exact figure is the true doubling time for annual compounding. The other two are approximations, and showing them together makes the shortcut's error visible instead of leaving it implicit.
72 divides evenly by the common rates 6, 8, 9, and 12, so 72 / r often produces a clean round number, and it is calibrated to sit within about 1% of the exact figure for rates near 6-8%. The 69.3 rule is ln(2) x 100, which is exact for continuous compounding but yields awkward numbers like 8.66 that are harder to compute mentally.
The Rule of 72 exists for mental math: 72 divides evenly by 6, 8, 9, and 12 and is most accurate near 6-8%. The 69.3 rule is ln(2) x 100 and matches continuous compounding exactly. The third figure is the precise answer for annual compounding, so the errors of both shortcuts are right there to see.
Not with this calculator - it is built around doubling. There is a common extension called the Rule of 114 for tripling, but the reliable general formula is t = ln(n) / ln(1 + r) for an n-fold increase. For any multiple other than two, that formula is the route to take.
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