The formula A=P(1+r)t is used to show the total amount owed for a loan with a simple annual interest rate.Solve for r.

We are asked to express r in terms of A, P, and t.

We first divide both sides of the equation by t, which gives us

                                         
                     [tex]\displaystyle{ \frac{A}{t}=P(1+r) [/tex], 


then, dividing both sides by P, we have

                     [tex]\displaystyle{ \frac{A}{Pt}=1+r [/tex].

Swap the sides:

                    [tex]\displaystyle{ 1+r= \frac{A}{Pt}[/tex] 
      
Finally subtracting 1 from both sides gives us

                     [tex]\displaystyle{ r=\frac{A}{Pt}-1[/tex].