Question

The balance of account A for an initial principal of P invested for t years in an account that earns a simple interest rate of r is given by A=P(1+rt)
. Solve the formula for t and simplify.

Answer 1

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

1. **Isolate the term involving \( t \)**:
Start by dividing both sides by \( P \) (assuming \( P \neq 0 \)):
\[
\frac{A}{P} = 1 + rt
\]

2. **Subtract 1 from both sides**:
\[
\frac{A}{P} - 1 = rt
\]

3. **Combine the terms on the left side**:
To subtract 1 from the fraction, we can express 1 as \( \frac{P}{P} \):
\[
\frac{A - P}{P} = rt
\]

4. **Isolate \( t \)**:
Now, divide both sides by \( r \) (assuming \( r \neq 0 \)):
\[
t = \frac{A - P}{Pr}
\]

Thus, the simplified formula for \( t \) is:
\[
t = \frac{A - P}{Pr}
\]