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

### Step-by-Step Solution

1. **Start with the formula**:
   \[
   A = P(1 + rt)
   \]

2. **Divide both sides by \( P \)** to isolate the term with \( r \):
   \[
   \frac{A}{P} = 1 + rt
   \]

3. **Subtract 1 from both sides** to further isolate \( rt \):
   \[
   \frac{A}{P} - 1 = rt
   \]

4. **Divide both sides by \( t \)** to solve for \( r \):
   \[
   r = \frac{\frac{A}{P} - 1}{t}
   \]

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

### Final Answer
\[
r = \frac{A - P}{Pt}
\]

Would you like further details or have any questions?

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Here are five related questions to expand on this topic:

1. What is the formula for \( t \) 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 \( A \), \( P \), and \( t \), how would you substitute them to find \( r \)?
4. What units should \( t \) have in this formula?
5. How would you interpret a negative value for \( r \) 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.

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

Learn how to solve for the interest rate (r) in the simple interest formula A = P(1 + rt). This step-by-step solution includes algebraic concepts relevant for high school students and covers simplifying and rearranging equations.

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