there are no chances for bitcoin to jump to $20k in the near future. Now there are no huge bumps in the price and the reason is that people are not so interested as they were in the last year. Due to low investment cap and low demand the price will not grow fast and $20k is a big price for bitcoin. Due to the current situation of the market it is clear that it will take long time to hit this level.
Well, that depends on how near the future you are talking about is like and for what it is worth, no one can really tell what becomes of bitcoin even in the next few seconds, so, the best answer to always give to situations like this is that at its own time, bitcoin would hit $20,000 and surpass it in the long run, as that is one thing I believe would happen eventually at some point as long as development and adoption keeps increasing.
many predict that the value of bitcoin will rise at the end of this year, and that makes me sure that the value of bitcoin is always rising every year, it could happen in the first quarter of next year
The value may rise at the end of the year, but does not mean it would be able to have enough power to go test the previous ATH. It is, I am sure bitcoin may still want to try out the bottom over again and then see how it is possible to break it lower but there could be some sideways movement or some upward movement before then and that in its own should be something to expect, but not like an exact price should be expected as no one can certainly know.