It's difficult to predict for the 100 years, but as of now, it's well and good so for the next years no problem at all it can operate smoothly.
No one can even say any thing about after before 100 year, we even cannot predict about fiat currency before 100 years before. But still we can say that bitcoin is a new emerging currency and people are still too much interested in bitcoin and therefore they are willing to invest more and more money in bitcoin and that is the reason that we can expect that the price of bitcoin will even survive after 100 Years.