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 given formula for simple interest: \(I = Prt\).
2. Identify the variable to solve for, which is \(P\) in this case.
3. To isolate \(P\), divide both sides of the equation by the product \(rt\) (assuming \(rt \neq 0\)): \(\frac{I}{rt} = \frac{Prt}{rt}\).
4. Simplify the right side by canceling \(rt\) in numerator and denominator, leaving \(P\) alone: \(\frac{I}{rt} = P\).
5. Rewrite the equation to express \(P\) explicitly: \(P = \frac{I}{rt}\).

Key Concepts

Simple Interest Formula

The simple interest formula I = Prt calculates interest (I) earned or paid on a principal amount (P) over time (t) at an interest rate (r). Understanding this formula is essential to manipulate and solve for any variable within it.

Solving for a Variable in an Equation

Solving for a variable involves isolating that variable on one side of the equation using algebraic operations such as multiplication, division, addition, or subtraction. This skill is crucial to rewrite formulas to express a specific variable explicitly.

Handling Variables in Denominators

When variables appear in denominators, it is important to ensure the denominator is not zero to avoid undefined expressions. This concept helps maintain the validity of the solution when rearranging formulas.