The Rule of 72 for compound interest

Within the financial community, the Rule of 72 is used as a quick and accurate tool to predict how fast your money will grow, how much interest you will need to earn to reach your goal and how inflation can affect your savings. Here's how it works:

This formula assumes that the interest (or inflation) rate remains the same throughout the period. But, even with rate fluctuations, using average rates the Rule of 72 can give you relatively accurate information and be a helpful tool in your financial planning.

from Texas A&M University System News, January, 1993

(C) copyright Texas A&M University System; reproduced here for a private educational purpose

Why does this rule work?