Let's solve for the variable [tex]\( P \)[/tex] in the future value formula for simple interest given by [tex]\( A = P(1 + r t) \)[/tex]. Here, [tex]\( A \)[/tex] represents the future value, [tex]\( P \)[/tex] is the present value (or principal), [tex]\( r \)[/tex] is the interest rate, and [tex]\( t \)[/tex] is time.
To isolate [tex]\( P \)[/tex], follow these steps:
1. Start with the given formula:
[tex]\[
A = P(1 + r t)
\][/tex]
2. To solve for [tex]\( P \)[/tex], we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by [tex]\( (1 + r t) \)[/tex]:
[tex]\[
\frac{A}{1 + r t} = P
\][/tex]
3. Rearrange the equation to express [tex]\( P \)[/tex] as the subject:
[tex]\[
P = \frac{A}{1 + r t}
\][/tex]
Hence, the correct formula for [tex]\( P \)[/tex] is:
[tex]\[
P = \frac{A}{1 + r t}
\][/tex]
This result indicates that to find the present value [tex]\( P \)[/tex], you need to divide the future value [tex]\( A \)[/tex] by the term [tex]\( (1 + r t) \)[/tex], which accounts for the interest rate and the time period.
Among the provided options, the correct one is:
[tex]\[
P = \frac{A}{1 + r t}
\][/tex]
