To determine the amount of money that Mike Kohl originally invested, we'll follow the steps involved in calculating the principal in a simple interest scenario.
Given:
- Interest earned ([tex]\(I\)[/tex]) = [tex]$240
- Annual interest rate (\(R\)) = 9% or 0.09 (in decimal form)
- Time period (\(T\)) = 6 months, which is \(0.5\) years
Simple interest formula:
\[ I = P \times R \times T \]
Where:
- \( I \) is the interest earned
- \( P \) is the principal amount (the amount originally invested)
- \( R \) is the annual interest rate (in decimal form)
- \( T \) is the time period in years
We need to rearrange this formula to solve for \( P \).
\[ P = \frac{I}{R \times T} \]
Step-by-step solution:
1. Calculate the interest rate for the 6-month period:
\[
R_{\text{6 months}} = R \times T = 0.09 \times 0.5 = 0.045
\]
2. Plug the values into the rearranged formula to solve for \( P \):
\[
P = \frac{I}{R_{\text{6 months}}} = \frac{240}{0.045}
\]
3. Perform the division:
\[
P = \frac{240}{0.045} = 5333.33
\]
Thus, the amount of money that Mike Kohl originally invested is $[/tex]5,333.33.
So the correct answer is:
d. $5,333.33
