You're correct, for my calculation, I assumed that all cells have the same age and live for the exact same time, which is bullshit in a living system.

And technically, all cells come from the same very fist cell anyway. As cells can't be created out of nothing, there is no way we become an "entirely new person", at least not biologically/naturally (if you add cells from a diffent person, it might look slightly different but I'm not going into this philosophical debate).