If I am considering a long-term investment that earns 10% APR, how long will it take for my investment to quadruple?;)

Approx 14.5 years.

To get an exact answer you need to solve the equation:

(1 + i) ^ N = 4


You can solve using logarithms to find that N = 14.54 years.

A simpler way to estimate this is to use "the rule of 72." Divide the interest rate into 72, and the result is the number of years it takes for an investment to double. At 10% the investment doubles in 72/10 = 7.2 years. Hence in another 7.2 years it doubles again. So a quick estimate (without having to use logarithms) yields 14.4 years.