Well I'm not sure it's plain English, but I can show you the algebra.
(P0-p) + i(P0-p) = P0 -p +P0i -pi
Now lets start with the second equation and multiply out
(PO-p)(1+i) = P0 + P0i -p -pi
So they are equivalent.
What you'll have after one year (P1) is what you had at the beginning of that year (P0) minus what you took out (p), but added to that the amount of interest you received on your stash, which is roughly the interest rate (i ) times your original fund size (P0) minus what you took out (p).