Change the subject of the formula s = p (1 + rt) to t.

If we're changing the subject to t, we want to get t on it's own. 

S = P(1 + rt) 

Since we can't do anything with the parenthesis, we have to start with the division/multiplication. Divide both sides by P:

S = 1 + rt
P

Next we want to get rid of the 1, so subtract 1 from both sides:

S   -  1  = rt
P

finally, divide both sides by r

(S/P) - 1 = t
      r 

so:

t = (S/P) - 1
         r