Let's solve the given problem step-by-step:
We need to evaluate the expression:
[tex]\[ 600\left[ \frac{1 - (1 + 0.02)^{-12}}{0.02} \right] \][/tex]
### Step 1: Calculate the term [tex]\( (1 + 0.02)^{-12} \)[/tex]
First, add 1 to the interest rate:
[tex]\[ 1 + 0.02 = 1.02 \][/tex]
Next, raise 1.02 to the power of -12:
[tex]\[ 1.02^{-12} \approx 0.7884931755816562 \][/tex]
### Step 2: Subtract this result from 1
[tex]\[ 1 - 0.7884931755816562 = 0.2115068244183438 \][/tex]
### Step 3: Divide by the interest rate (0.02)
Now, we take the result from Step 2 and divide it by the interest rate:
[tex]\[ \frac{0.2115068244183438}{0.02} = 10.57534122091719 \][/tex]
### Step 4: Multiply by the monthly payment ($600)
Finally, multiply the result from Step 3 by the monthly payment:
[tex]\[ 600 \times 10.57534122091719 = 6345.204732550313 \][/tex]
So, the detailed step-by-step solution gives us the final result:
[tex]\[ 600\left[ \frac{1-(1+0.02)^{-12}}{0.02} \right] = 6345.204732550313 \][/tex]
