Having bought basic archery gear for 3 people in the last year, unless you're talking about a toy longbow, $20 is not going to get you anywhere. Even buying the absolute necessities for a basic barebow recurve setup, let's list things off:

Riser, plunger, arrow rest, limbs, string, arrows, finger tab. That's the absolute bare minimum. You'll also probably want an arm guard unless you don't value your forearms. You can't do this for less than US$150-$200, unless you find someone basically giving away second hand equipment.