Where does the rule of 72 come from?

Answer 1

The equation to determine the future value of an amount of month that is earning interest is FV=PV*(1+r)^t.

FV = Future Value

PV = Present Value

r = interest rate per period

t = number of periods

If you divide both side by PV you get FV/PV=(1+r)^t.

The rule of 72 is used to calculate how long it takes money to double in value. Therefore FV/PV =2

2=(1+r)^t

Take the natural log of both sides and you get...

ln(2) = ln(1+r)^t which equals ln(2) = t*ln (1+r)

For small values of r (remember this is a percentage) ln(1+r) ~ r

r*t = ln(2)

r*t = 0.693. So technically is should be the rule of 69.3. However, 72 is evenly divisible by far more numbers, and since this is for doing ball park numbers in your head, it is close enough. However feel free to use 70 as well if it works better (multiples of 5 or 7).

Eagle