To solve for [tex]\(P\)[/tex] in the simple interest formula [tex]\(I = Prt\)[/tex], follow these steps:
1. Start with the given formula:
[tex]\[
I = Prt
\][/tex]
Here, [tex]\(I\)[/tex] represents the interest, [tex]\(P\)[/tex] is the principal (the initial amount of money), [tex]\(r\)[/tex] is the rate of interest per period, and [tex]\(t\)[/tex] is the time the money is invested for.
2. We need to isolate [tex]\(P\)[/tex] on one side of the equation. To do this, divide both sides of the equation by [tex]\(rt\)[/tex]:
[tex]\[
\frac{I}{rt} = \frac{Prt}{rt}
\][/tex]
3. Simplify the right side of the equation. Since [tex]\(rt\)[/tex] cancels out on the right side, we have:
[tex]\[
\frac{I}{rt} = P
\][/tex]
4. We have successfully isolated [tex]\(P\)[/tex] and found the expression:
[tex]\[
P = \frac{I}{rt}
\][/tex]
So the correct expression for [tex]\(P\)[/tex] is:
[tex]\[
P = \frac{I}{rt}
\][/tex]
From the given options, the correct one is:
[tex]\[
P = \frac{I}{rt}
\][/tex]
