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To solve for \( r \) in the formula \( A = P(1 + rt) \), follow these steps:

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

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

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

So, the answer is:
\[
r = \frac{A - P}{Pt}
\]

Would you like a more detailed explanation, or do you have any additional questions?

Here are some related questions that could help deepen your understanding:

1. How can this formula for \( r \) be applied in a practical financial scenario?
2. What is the formula if we need to solve for \( P \) instead of \( r \)?
3. How does this formula change if the interest is compounded rather than simple?
4. What are the limitations of using simple interest versus compound interest?
5. How would you solve for \( t \) if it were the unknown variable?

**Tip**: When solving for a specific variable, carefully isolate terms step-by-step, performing inverse operations in reverse order of the operations in the equation.

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

Learn how to solve for the rate of interest (r) using the simple interest formula A = P(1 + rt). This solution provides a step-by-step guide to isolating r and is suitable for high school students studying algebra and finance concepts.

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