Well, if you double a dollar every year for 20 years, you will end up with $1,048,576
Of course. But you're taking what I said out of context.
Commodity_Trader implied that compounding returns had something to do with being able to double his/her investment every year. I take this to imply the idea that after n years, there will have been an average doubling of the amount of initial investment per year, measured at year n, resulting from compounding returns. So, for example, investing $1 will lead to $20 after 10 years, or $40 after 20 years, or $60 after 30 years, etc. (i.e., essentially $2/year for n years). I know this is somewhat of a convoluted concept. But it is nonetheless a well-posed problem with a simple solution: the amount of annual returns (x) necessary to achieve this at year n is x = (2n)^(1/n)-1.