Math Problem Statement

Using the interest formula A = P(1 + rt), solve for the indicated variable r.

Solution

To solve for rr in the interest formula given by A=P(1+rt)A = P(1 + rt), let's go through the steps:

Step-by-Step Solution

  1. Start with the formula: A=P(1+rt)A = P(1 + rt)

  2. Divide both sides by PP to isolate the term with rr: AP=1+rt\frac{A}{P} = 1 + rt

  3. Subtract 1 from both sides to further isolate rtrt: AP1=rt\frac{A}{P} - 1 = rt

  4. Divide both sides by tt to solve for rr: r=AP1tr = \frac{\frac{A}{P} - 1}{t}

  5. Simplify the expression: r=APPtr = \frac{A - P}{Pt}

Final Answer

r=APPtr = \frac{A - P}{Pt}

Would you like further details or have any questions?


Here are five related questions to expand on this topic:

  1. What is the formula for tt if we are solving for time in the interest formula?
  2. How would this formula change if it were compound interest instead of simple interest?
  3. If you know the values of AA, PP, and tt, how would you substitute them to find rr?
  4. What units should tt have in this formula?
  5. How would you interpret a negative value for rr in practical terms?

Tip: Remember, when working with interest formulas, be clear whether you're using simple or compound interest as they have different formulas.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simple Interest
Solving for Variables

Formulas

A = P(1 + rt)
r = (A - P) / (Pt)

Theorems

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Suitable Grade Level

Grades 9-12