Since bitcoin values has been decided by the free market It may have a chance to still survive after 100 years thou the value may not be as high as today since I believe that bitcoin was already been replaced by more advance cryptocurreny.
Well we live to see, but 100 years from now is quite too long a time for us to speculate about the fate of bitcoin because technologies that changes the world and how we do things can emerge within a year or two and render it completely useless and so we should give it some room before any speculations.