The price could go up that much but I would suggest be careful about it when that happens, if the price goes up anything above 15k there will be a huge gap in the bottom which means it could literally freefall back down under 10k and that would hurt many investors. That is why I highly suggest people to buy now and sell then instead of actually buying then, if you see bitcoin going up to 15k or more than do not buy it, it could still go even higher but that is a big risk compared to right now.
I am not saying bitcoin won't reach 20k or higher, it will but if it does a sudden move without closing the gaps then it will eventually fall which will be another bear run for months for us, it should slowly go up and down in order to reach highers while closing the gaps in between.