Sure, let's go through this step-by-step:
1. Identify the given variables:
- Interest earned ([tex]\(I\)[/tex]): \[tex]$24
- Annual interest rate (\(r\)): 6% (which is 0.06 in decimal form)
- Time (\(t\)): 4 years
2. Understand what we need to find:
- The principal balance (\(P\)), which is the initial amount of money that was deposited.
3. Use the formula for simple interest:
\[
I = P \cdot r \cdot t
\]
We need to rearrange this formula to solve for \(P\):
\[
P = \frac{I}{r \cdot t}
\]
4. Substitute the known values into the rearranged formula:
\[
P = \frac{24}{0.06 \cdot 4}
\]
5. Calculate the denominator first:
\[
0.06 \cdot 4 = 0.24
\]
6. Divide the interest earned by this product to find the principal:
\[
P = \frac{24}{0.24} = 100.0
\]
Therefore, Imani's principal balance is \(\$[/tex]100.00\).
From the given options, the correct answer is:
[tex]\[
\boxed{100.00}
\][/tex]
