04.15.07
Rule of 72
Logarithms are one of the most universally hated/feared topics in high school mathematics. The notation is arcane, their properties are confusing, and few teachers (let alone students) will even attempt to estimate them without a calculator. Unfortunately they are indispensable for asking one very useful investment question: “Assuming exponential growth of R% per year, how long will it take for $X to grow into $Y?”
Luckily, there is a simple rule of thumb that you can calculate using pencil and paper. At a growth rate of R% per year, it takes approximately 72/R years for an investment to double. Investing at a 4% rate of return? Your money will double in approximately 72/4 or 18 years. Wait 36 years and it will redouble (think Backgammon or Bridge) to *four* times the initial investment — thus the power of starting your retirement savings early.