Depending on the year of the bike it may not have a built in derailleur hanger. Chances are it has a bolt on hanger. If this is the case you can buy a new derailleur for $15 or so. Do not spend any more money than that on your Schwinn. Its not worth it. I've seen used bikes in second hand stores and LBS's with 7 or 8 speeds and indexed shifting for less than $100.