Bitcoin need at least 10-20 years to come into mainstream. Price should be +$20,000. But we'll see.
We will not have to wait that long. Things are developing very fast these days and if Bitcoin will become mainstream like other currencies that will happen much sooner, 5-7 years at most.
Altgough I'm not sure about the price, it seems a bit too excessive. It will go up a lot with time, that I agree. Still, that much....But like you've said we'll see.
I think $20,000 is a reasonable price for Bticoin if it will be fully adopted. Actually the price might go much higher if most people would start trusting Bitcoin more than other currencies, but we can't guarantee that that will happen. But $20k might be reached due to wider adoption alone: people will start buying coins and since we can't make more of them than is made in a certain period of time, the natural response to the higher demand will be the rising of the price.
There are a lot of ifs for that price to be attained. Achieving the trust of people is not easy. People trust gold (and dollars) because it has been around for a long time. Bitcoin was born yesterday,
The new 0.13 Core Client has been released. The SegWit has been implemented. So the price could rise.