Certainly! Let's solve this step-by-step:
a. Find the interest earned:
To calculate the interest earned using the simple interest formula, we use the following formula:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
- Principal (P): This is the initial amount of money deposited, which is [tex]$2000.
- Rate (R): This is the interest rate per year, which is 3.5%. To convert this percentage to a decimal, we divide by 100: \( \frac{3.5}{100} = 0.035 \).
- Time (T): This is the time period for which the money is invested, which is 4 years.
Now, plug these values into the formula:
\[ \text{Interest} = 2000 \times 0.035 \times 4 \]
\[ \text{Interest} = 280.0 \]
So, the interest earned over 4 years is $[/tex]280.0.
b. Find the balance of the account:
The balance of the account is the sum of the principal amount and the interest earned. We use the following formula:
[tex]\[ \text{Balance} = \text{Principal} + \text{Interest} \][/tex]
We already calculated the interest to be [tex]$280.0. Now, add this to the principal amount:
\[ \text{Balance} = 2000 + 280.0 \]
\[ \text{Balance} = 2280.0 \]
Therefore, the balance of the account after 4 years is $[/tex]2280.0.
So, to summarize:
- The interest earned over 4 years is [tex]$280.0.
- The balance of the account after 4 years is $[/tex]2280.0.
