To simplify [tex]\( 600(1+0.03)^{12} \)[/tex], let's break down the steps:
1. Understand the Expression: The expression [tex]\( 600(1+0.03)^{12} \)[/tex] represents an amount of money growing with compound interest. Here, 600 is the initial amount, 0.03 is the interest rate, and 12 is the number of compounding periods.
2. Calculate the Growth Factor:
[tex]\[ 1 + 0.03 \][/tex]
[tex]\[ = 1.03 \][/tex]
3. Raise the Growth Factor to the Power of 12:
[tex]\[ 1.03^{12} \][/tex]
This calculation might be complex to do manually, but it's essential to understand that it represents the total growth over 12 periods.
4. Multiply by the Initial Amount:
[tex]\[ 600 \times 1.03^{12} \][/tex]
Performing these steps, we obtain the approximate value:
[tex]\[ 600(1+0.03)^{12} \approx 600 \times 1.03^{12} \approx 855.46 \][/tex]
Thus, [tex]\( 600(1+0.03)^{12} \)[/tex] simplifies to about 855.46. Therefore, the correct answer from the given options is:
- About 855.46
