There is no way to tell you how long would it take you to get to 200k power. It took me a bit more then two and the half year to get to 350k as f2p.

But now its much easier and faster to power up as a f2p. 80% of the power functions didnt exist when i started. And the stuff that existed were much harder to get ( keys-magatamas-runes ).

But if i had to guess it would take you maybe 15-18 months. But thats only if you knew how to play the game. How to farm max CPs as a f2p. Where,when and on what to spend your CPs for most of the power gain.

But as long as you have fun it really doesnt matter how much time its going to take, Just dont rush while playing. Leveling to fast wont do you any good if you dont have power.