Obviously, this will be a low rate, but I have seen some say that as low as 1BC=$13.5k, is this plausible?
No, you can not buy anymore at that rate because the price has already increased by more than 20% of that.
It is now being tradeable at aproximate $16,800 at the moment, so no, you are a little bit late to the party.
If you really want to start investing, do it now before it touches twenty thousand dollars again, it is just my advice. Bitcoin will always go up, only that it has some obstacles on the middle, and it will keep happening forever.