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