# 88Pro Thinking

## Rule of 72!

After reading Dave’s article on “Pipelines”, I got hold of Programming Pearls by Jon Bentley. I came across a very interesting piece of text in the Column “The Back of the Envelope” where he talks about basic estimation skills. Here it is:

I first learned about the “Rule of 72” in a course on accounting. Assume that you invest a sum of money for y years at an interest rate of r percent per year. The financial version of the rule says that if r x y = 72, then your money will roughly double. The approximation is quite accurate: investing \$1000 at 6 percent for 12 years gives \$2012, and \$1000 at 8 percent for 9 years gives \$1999.

The rule of 72 is handy for estimating the growth of any exponential process. If a bacterial colony in a dish grows at the rate of three percent per hour, then it doubles in size every day.

Suppose that an exponential program takes ten seconds to solve a problem of size n=40, and that increasing n by one increases the run time by 12 percent (we probably learned this by plotting growth on a logarithmic scale). The rule of 72 tells us that the run time doubles when n increases by 6.
[By Jon Bentley, Programming Pearls, Column 7, Page 67]

Isn’t it interesting to see how rules from financial world can be applied to other real world estimations?

posted by 88Pro / Monday, June 07, 2004  