From:
http://usmilitary.about.com/od/officerjo2/a/bdcp.htm
"Service Obligation: 4 yrs Active Duty from enlistment; superceded upon commission by applicable desig. requirements "
For your question "Could you choose to stay active for the 4 reserve years?"
Somebody correct me if I am wrong, but you can re-enlist to stay active after your original contract is over (obvious). The 4 year reserve duty, means if they still want to keep you active or call you back up to active duty they can, but it's not like you're in a reserve unit with drill every month.