I saw this post about the rule of 72 - basically, you can estimate how long it'll take your money to double at a set interest rate by dividing 72 by the rate. So at 3% interest, it'll take approximately 72/3 or 24 years to double.
So, I started playing with the math (x is the number of years and y is the interest rate) . . .
- (1+y/100)^x = 2
- x ln(1+y/100) = ln2
- x = (ln2)/ln(1+y/100)
And that's where I get stuck . . . I can plot it and see that 72/y approximates (ln2)/ln(1+y/100). Maybe that's the way to do it? Plot the graph, realize that it's an inverse curve, and fit it?