Odds are... never.
I was checking on Bitcoinwisdom's mining calculator, and even with a 1% increase in difficulty every 2016 blocks and a 1% pool fee, assuming free... you'll never get back your $20 investment (assuming free shipping). The closest you'd get to breaking even (according to that website) is $19.98 in red. Mining with that for profit isn't worth it. At all. It might be good to get started, to see how mining works, or just for fun. But not for profit.

I repeat, you will never break even if you mine with that.