Here are the steps to follow when it comes to solving for t. This is not the only way to do so
Step 1) A = P*(1+rt)
Step 2) A = P*(1)+P*(rt)
Step 3) A = P+P*(rt)
Step 4) A-P = P+P*(rt)-P
Step 5) A-P = P*(rt)
Step 6) A-P = t*(Pr)
Step 7) (A-P)/(Pr) = (t*(Pr))/(Pr)
Step 8) (A-P)/(Pr) = t
Step 9) t = (A-P)/(Pr)
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and here are the explanations for each step
Step 1) Nothing to do here. This is the original equation
Step 2) Distribute the outer P term into each inner term (1 and rt)
Step 3) Multiply P and 1 to get P*(1) = P
Step 4) Subtract P from both sides
Step 5) Simplify. Note how the P-P on the right side becomes 0P = 0 which goes away on the right side
Step 6) Rearrange the terms on the right side to go from P*(rt) to t*(Pr).
Step 7) Divide both sides by Pr.
Step 8) Simplify. The Pr term on the right side divides with itself to get 1. Because 1 times anything is itself, we effectively have Pr cancel out and go away.
Step 9) Flip the equation so that the t is on the left side
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The answer is t = (A-P)/(Pr) which can be written as
The parenthesis in the equation t = (A-P)/(Pr) are important because we are specifying that we are dividing all of "A-P" all over all of "Pr"