How long until you are competent?

I'm a high school senior who is very interested in programming as a backup option for if my acceptance to music school does not happen, or happens with too little scholarship money to afford it. I'm pretty big on math, and have done a bit of Learn Python The Hard Way. I guess my question is, with or without college, how long does it seem to take until most people are able to begin programming for money?

I know it's a lifelong-learning experience, but surely there has to be a point in which you can support yourself on your work.

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