Answer :
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
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
