If you've got the money, do it. 3 Months from home is little compared to the chance to advance your education, travel in a different continent, make new friends and experience foreign culture. Considering you will leave home eventually to take on your own life, a nice 3 month learning experience, which will no doubt improve your concept of culture and much more, is absolutely worth it.
If you've got the money, definitely do it. If it's free, don't turn down a major experience for a short-lived inevitable feeling.
do it