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?".