YES! It's SOOOOOOOOOO worth it! Every cent! Just having had the experience of being in a foreign country for a little longer than the typical tourist thing changes you, and broadens your horizons.
Last semester, I went to Rome to study art, architecture, and urban planning. None of the courses counted towards my major except for one (Architecture of Ancient Rome), and it was pretty hard work, but it was THE most amazing experience of my life. I think my parents were a little hard to convince about being abroad post 9/11 (there were terrorist attacks in Rome while I was there), but the fact that this program was less than a normal semester's tuition helped.
It's possible that being abroad might help you find some concrete direction if you don't already have it. One of the most important things that came out of my Rome trip is that I realized that I wanted to be an architect more than anything. Now, I'm applying to graduate programs in Architecture. Similar situations have happened to other people I know--the electives they took, although they had nothing to do with their major at that time, directed them to something they had never thought of.