Let's solve the problem step-by-step to find out the balance after 8 years when [tex]$1200 is invested at 3% simple interest.
1. Identify the Variables:
- Principal (P): $[/tex]1200
- Rate of interest (r): 3% per year or 0.03 in decimal form
- Time (t): 8 years
2. Understand the Simple Interest Formula:
The formula for calculating simple interest is:
[tex]\[
\text{Simple Interest} = P \times r \times t
\][/tex]
You can then find the total balance by adding the simple interest to the principal amount.
3. Calculate the Simple Interest:
[tex]\[
\text{Simple Interest} = 1200 \times 0.03 \times 8
\][/tex]
By calculating the above expression, you get:
[tex]\[
\text{Simple Interest} = 1200 \times 0.24
\][/tex]
[tex]\[
\text{Simple Interest} = 288
\][/tex]
4. Calculate the Total Balance:
Add the simple interest to the principal to get the total balance:
[tex]\[
\text{Total Balance} = \text{Principal} + \text{Simple Interest}
\][/tex]
[tex]\[
\text{Total Balance} = 1200 + 288
\][/tex]
[tex]\[
\text{Total Balance} = 1488
\][/tex]
So, the balance after 8 years will be [tex]$1488. Therefore, the correct answer is:
$[/tex]1488
