Answer :

[tex]S=P(1+rt)[/tex]

start by dividing by p on both sides

[tex]\begin{gathered} \frac{S}{P}=\frac{P}{P}(1+rt) \\ \frac{S}{P}=1+rt \end{gathered}[/tex]

substract 1 on both sides

[tex]\begin{gathered} \frac{S}{P}-1=1+rt-1 \\ \frac{S}{P}-1=rt \end{gathered}[/tex]

Divide by t on both sides to solve for r

[tex]\begin{gathered} (\frac{S}{P}-1)(\frac{1}{t})=\frac{rt}{t} \\ \frac{S}{Pt}-\frac{1}{t}=r \end{gathered}[/tex]

ANSWER

[tex]r=\frac{S}{Pt}-\frac{1}{t}[/tex]

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