If S=P(1+rt), make t the subject formula.

Solve for t:
S = P (r t + 1)

Reverse the equality in S = P (r t + 1) in order to isolate t to the left-hand side.
S = P (r t + 1) is equivalent to P (r t + 1) = S:
P (r t + 1) = S

Divide both sides by a constant to simplify the equation.
Divide both sides by P:
r t + 1 = S/P

Isolate terms with t to the left-hand side.
Subtract 1 from both sides:
r t = (S - P)/P

Solve for t.
Divide both sides by r: 

t = (S - P)/(P r)

If S=P(1+rt), make t the subject 

Divide both sides by P

S / P  =  1 + rt       

Subtract 1 from both sides

S / P  - 1    =  rt     

Divide both sides by  r

S / (Pr)  - 1 / r   = t