c. \( A=P+P r t \quad \) for \( P \)

To solve for \( P \) in the equation \( A = P + P r t \), you first need to factor out \( P \) on the right side, giving you \( A = P(1 + rt) \). To isolate \( P \), simply divide both sides by \( (1 + rt) \), resulting in \( P = \frac{A}{1 + rt} \). Voilà! You've found \( P \) in terms of \( A \), \( r \), and \( t \). This equation describes a simple interest scenario, where \( A \) is the total amount, \( r \) is the interest rate, and \( t \) is the time in years. Understanding how to manipulate this formula can help you grasp how much principal you need to invest to reach a certain amount after earning interest, making budgeting and financial planning feel a lot less daunting!