Question

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 and simplify.

Explanation:

Step1: Identify the target variable

We need to solve the formula \( A = P(1 + rt) \) for \( t \). So, we aim to isolate \( t \) on one side of the equation.

Step2: Divide both sides by \( P \)

To start isolating \( t \), divide both sides of the equation by \( P \) (assuming \( P
eq0 \)). This gives us:
\( \frac{A}{P}=1 + rt \)

Step3: Subtract 1 from both sides

Next, subtract 1 from both sides to get the term with \( t \) alone on one side:
\( \frac{A}{P}- 1=rt \)
We can rewrite \( 1 \) as \( \frac{P}{P} \) to have a common denominator:
\( \frac{A - P}{P}=rt \)

Step4: Divide both sides by \( r \)

Finally, divide both sides of the equation by \( r \) (assuming \( r
eq0 \)) to solve for \( t \):
\( t=\frac{A - P}{Pr} \)

Answer:

\( t = \dfrac{A - P}{Pr} \)