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.
