Does doing an undergraduate semester exchange abroad improve chances of getting into top universities? I am a math undergraduate student from India, from one of the IITs. I have an opportunity to go for a semester exchange at some Universities in Germany, France and Switzerland, for a single semester. I am interested in pursuing further studies in pure mathematics at a top university abroad. I wanted to ask how much would a semester at an excellent university help me in getting into the masters or Phd program of the same University, or for that matter even other top universities.

How much of an impact would a semester at an excellent university have on the chances of acceptance for masters and Phd programs at top universities?

Edit: Recent development and further information

I have been accepted as an exchange student at EPFL.(The question still remains)

Some background as to why I am asking the question - While the University is not taking any semester fees, the cost involved is significantly high, and would stretch my finances quite a bit. I want to evaluate what I would get out of, what would be a very significant monetary investment for me. Basically "Is it worth it?".
As JeffE says: It does not really matter whether you went somewhere and where did you go; it matters much more what have you done there. In general, having an Erasmus (or similar) semester abroad is not seen much as an advantage. Having a semester abroad accompanied by a publication with a professor there -- that's a different story, because it shows that you went there and really got some experience there.

However, if you spend the semester at a university at which you later apply for studies (which seems to be your case), you can get something from solely being there: the contacts and the knowledge of the environment. For instance: There are many PhD positions funded by various projects rather than by some general scholarships. It's mostly the project leaders who decide who gets the funding, and knowing them in person etc. can help. Still, you need to do more than just sit there at the lectures for 15 weeks.