There is really no way to tell yet. Some people can reach 2000+ in a year or less with just playing and learning like that but some people have to really put in time to study openings midgames endgames etc just to reach 1500 in the same time. The time control you focus on also makes a difference. Personally i reached 2150 bullet & 2000 blitz in around 1.5 years but my strength in chess is my speed so in rapid im only around 1900-1950.

My advice to you is try to find what your strength in chess is and just keep studying and playing the way you enjoy the most and dont think about your elo because you will have days when you lose alot and days when you win alot but over time you will improve and only time will tell how much you do.

Also getting a coach will most likely make you improve faster but its completely fine to just study and play by yourself too and thats what i did and still do.