Answer :
Certainly! Let's break down the solution step-by-step for Charlene's investment at 6% simple interest for 3 years.
Step 1: Understanding the concepts
1. Principal (P): This is the initial amount of money invested. In this case, it is \[tex]$3300. 2. Rate (R): This is the annual interest rate. Here, it is 6%. 3. Time (T): This is the period for which the money is invested. Here, it is 3 years. 4. Simple Interest (I): Simple interest is calculated using the formula: \[ I = P \times R \times T \] Step 2: Calculate the Simple Interest First, we need to convert the percentage rate into a decimal. The rate given is 6%, which can be written as 0.06 in decimal form. Using the formula for simple interest: \[ I = P \times R \times T \] Substituting the given values into the formula: \[ I = 3300 \times 0.06 \times 3 \] Calculating this step-by-step: \[ 3300 \times 0.06 = 198 \] \[ 198 \times 3 = 594 \] Thus, the simple interest earned over 3 years is \$[/tex]594.
Step 3: Calculate the Final Amount
The final amount (A) after the investment period is the sum of the principal and the interest earned. We use the formula:
[tex]\[ A = P + I \][/tex]
Substituting the values we have:
[tex]\[ A = 3300 + 594 \][/tex]
Calculating this:
[tex]\[ A = 3894 \][/tex]
Summary
1. The simple interest earned over 3 years is \[tex]$594. 2. The total amount of money Charlene will have after 3 years is \$[/tex]3894.
So, Charlene's investment yields a simple interest of \[tex]$594, and she will have a final amount of \$[/tex]3894 after 3 years.
Step 1: Understanding the concepts
1. Principal (P): This is the initial amount of money invested. In this case, it is \[tex]$3300. 2. Rate (R): This is the annual interest rate. Here, it is 6%. 3. Time (T): This is the period for which the money is invested. Here, it is 3 years. 4. Simple Interest (I): Simple interest is calculated using the formula: \[ I = P \times R \times T \] Step 2: Calculate the Simple Interest First, we need to convert the percentage rate into a decimal. The rate given is 6%, which can be written as 0.06 in decimal form. Using the formula for simple interest: \[ I = P \times R \times T \] Substituting the given values into the formula: \[ I = 3300 \times 0.06 \times 3 \] Calculating this step-by-step: \[ 3300 \times 0.06 = 198 \] \[ 198 \times 3 = 594 \] Thus, the simple interest earned over 3 years is \$[/tex]594.
Step 3: Calculate the Final Amount
The final amount (A) after the investment period is the sum of the principal and the interest earned. We use the formula:
[tex]\[ A = P + I \][/tex]
Substituting the values we have:
[tex]\[ A = 3300 + 594 \][/tex]
Calculating this:
[tex]\[ A = 3894 \][/tex]
Summary
1. The simple interest earned over 3 years is \[tex]$594. 2. The total amount of money Charlene will have after 3 years is \$[/tex]3894.
So, Charlene's investment yields a simple interest of \[tex]$594, and she will have a final amount of \$[/tex]3894 after 3 years.
