Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. I=Prt,for P (simple interest)

Verified step by step guidance

1. Start with the formula for simple interest: \( I = Prt \).
2. To solve for \( P \), you need to isolate \( P \) on one side of the equation.
3. Divide both sides of the equation by \( rt \) to get \( P \) by itself: \( P = \frac{I}{rt} \).
4. Ensure that \( rt \neq 0 \) to avoid division by zero.
5. Now, \( P \) is expressed in terms of \( I \), \( r \), and \( t \).

Key Concepts

Simple Interest Formula

The simple interest formula, I = Prt, calculates the interest earned or paid on a principal amount (P) over time (t) at a specific rate (r). In this formula, I represents the interest, P is the principal amount, r is the rate of interest per time period, and t is the time the money is invested or borrowed. Understanding this formula is crucial for solving for any of its variables.

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This process includes operations such as addition, subtraction, multiplication, and division applied to both sides of the equation. Mastery of these techniques is essential for solving equations like I = Prt for P, as it allows one to express P in terms of I, r, and t.

Assumption of Non-zero Denominator

In algebra, it is important to note that division by zero is undefined. The instruction to assume that the denominator is not zero ensures that any variable in the denominator does not take on a value that would make the equation invalid. This concept is critical when manipulating equations to avoid undefined expressions and to ensure valid solutions.