Question 1035061
f = p * (1+r)^n


f = future value
p = present value
r = interest rate per time period
n = number of time periods.


when you compound annually, r is the annual interest rate and n is the number of years.


if you divide both sides of the equation by p, you get:


f/p = (1+r)^n


if your present value doubles, then f/p = 2


you wind up with 2 = (1+r)^n


take the natural log of both sides of this equation to get:


ln(2) = ln(1+r)^n


since log(a^b) = b*log(a), your equation becomes:


ln(2) = n*ln(1+r).


solve for n to get n = ln(2) / ln(1+r).


when r = .03, this becomes n = ln(2) / ln(1.03)
when r = .04, this becomes n = ln(2) / ln(1.04)
when r = .06, this becomes n = ln(2) / ln(1.06)


solve for n and you get:


when r = .03, n = 23.45
when r = .04, n = 17.67
when r = .06, n = 11.90


using the rule of thumb, .....


when r = .03, n = 72/3 = 24
when r = .04, n = 72/4 = 18
when r = .06, n = 72/6 = 12


that's a pretty close estimate to the actual calculations.


rule of 72 looks like it works pretty good.