About

The Rule of 72 is a famous mental math shortcut used by investors to estimate the time required to double an investment at a fixed annual rate of interest. By simply dividing 72 by your expected return rate, you get a surprisingly accurate estimate of the years required.

However, as interest rates get higher (above 15-20%), the Rule of 72 loses accuracy. This tool calculates both the "Rule of 72" estimate and the "Precise Logarithmic" doubling time, helping you understand exactly when your portfolio or savings will hit that 2x milestone.

Formulas

The shortcut approximation is defined as:

t ≈ 72r

Where r is the percentage rate (e.g., 8 for 8%). The precise calculation is derived from the compound interest formula 2P = P(1+r/100)^t, solved for t:

t = ln(2)ln(1 + r/100)

Reference Data

Rate (%)	Rule of 72 Est.	Precise (Log)	Error Margin
1%	72.00 years	69.66 years	+3.4%
5%	14.40 years	14.21 years	+1.3%
8%	9.00 years	9.01 years	-0.1% (Best)
10%	7.20 years	7.27 years	-1.0%
20%	3.60 years	3.80 years	-5.3%
50%	1.44 years	1.71 years	-15.8%
100%	0.72 years	1.00 years	-28.0%

Frequently Asked Questions

Yes. You can use the Rule of 72 to calculate how long it takes for money to lose half its value by dividing 72 by the inflation rate. For example, at 6% inflation, prices double (and purchasing power halves) in approximately 12 years.

Mathematically, ln(2) is ~0.693, so 69.3 is the most accurate numerator for continuous compounding. However, 72 is used because it has many divisors (2, 3, 4, 6, 8, 9, 12), making it much easier to calculate mentally. 72 also happens to be more accurate for typical investment ranges (6-10%) due to discrete annual compounding.

Similar to the Rule of 72, the Rule of 115 estimates how long it takes for an investment to triple (3x) in value.