Using the interest formula Upper A equals Upper P left parenthesis 1 plus rt right parenthesis​, solve for the indicated variable.
Solve for t.

To solve the interest formula \( A = P(1 + rt) \) for the variable \( t \), follow these steps:

### Given Formula:
\[
A = P(1 + rt)
\]

### Step 1: Divide both sides by \( P \) to isolate the \( (1 + rt) \) term:
\[
\frac{A}{P} = 1 + rt
\]

### Step 2: Subtract 1 from both sides to isolate the \( rt \) term:
\[
\frac{A}{P} - 1 = rt
\]

### Step 3: Divide both sides by \( r \) to solve for \( t \):
\[
t = \frac{\frac{A}{P} - 1}{r}
\]

### Final Answer:
\[
t = \frac{A - P}{Pr}
\]

This formula gives the value of \( t \) in terms of \( A \), \( P \), and \( r \).

Would you like any details or have any questions about this process? Here are five related questions you might find useful:

1. How does the formula change if you're dealing with compound interest instead of simple interest?
2. What does each variable \( A \), \( P \), \( r \), and \( t \) represent in this formula?
3. Can you provide an example calculation using specific values for \( A \), \( P \), and \( r \)?
4. What is the difference between the interest formulas for simple and compound interest?
5. How does changing the interest rate \( r \) affect the time \( t \) required to reach a certain amount \( A \)?

**Tip:** Always double-check your formula manipulations by substituting values to see if the rearranged formula holds true.

Learn how to solve for the time (t) in the interest formula A = P(1 + rt) with a detailed step-by-step solution. This problem covers key concepts in interest calculations and equations. Suitable for students in Grades 10-12.

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