Certainly! Let’s break down the problem step-by-step to find the interest earned and the total amount accumulated when [tex]$6,400 is invested at an annual interest rate of 2.94% for a duration of 9 months.
### Step-by-Step Solution:
1. Identify the Principal (P):
- The initial amount invested is $[/tex]6,400.
2. Identify the Annual Interest Rate (R):
- The interest rate per year is 2.94%.
3. Convert the Interest Rate into Decimal Form:
- Since percentage (%) means per hundred, convert the rate by dividing by 100:
[tex]\[
R = \frac{2.94}{100} = 0.0294
\][/tex]
4. Identify the Time (T) in Years:
- The interest duration is given in months, so we convert the time period from months to years. Since there are 12 months in a year, 9 months is:
[tex]\[
T = \frac{9}{12} = 0.75 \text{ years}
\][/tex]
5. Apply the Simple Interest Formula:
- The formula for simple interest is:
[tex]\[
I = P \times R \times T
\][/tex]
- Substitute the values into the formula:
[tex]\[
I = 6400 \times 0.0294 \times 0.75
\][/tex]
6. Calculate the Interest Earned (I):
- Performing the multiplication:
[tex]\[
I = 6400 \times 0.0294 \times 0.75 = 141.12
\][/tex]
- The interest earned over 9 months is [tex]$141.12.
7. Calculate the Total Amount Accumulated:
- The total amount is the sum of the principal and the interest earned:
\[
\text{Total Amount} = P + I
\]
\[
\text{Total Amount} = 6400 + 141.12 = 6541.12
\]
### Summary:
- Interest Earned: $[/tex]141.12
- Total Amount Accumulated: [tex]$6541.12
Therefore, the interest earned on $[/tex]6,400 at an annual interest rate of 2.94% for 9 months is [tex]$141.12, and the total amount after 9 months is $[/tex]6541.12.
