PIS – 21.4gr in .22

With out me spending money on the wrong regulator does anyone have an idea what PSI I would need to do the following;

Shoot a 21.4gr .22 pellet through a 24″ barrel at 850-870FPS.

I am thinking it will be 1800 – 2000 but I really do not have a clue. It is important that I get these FPS as the pellet like it.