Let's evaluate the given expression step-by-step for [tex]\( k = 2 \)[/tex] and [tex]\( n = 10 \)[/tex].
### Step 1: Identify the values
[tex]\[
P = 12000, \quad r = 0.08, \quad k = 2, \quad n = 10
\][/tex]
### Step 2: Plug these values into the expression
[tex]\[
12000\left(1 + \frac{0.08}{2}\right)^{2 \cdot 10}
\][/tex]
### Step 3: Simplify the fraction inside the parentheses
[tex]\[
\frac{0.08}{2} = 0.04
\][/tex]
### Step 4: Add this value to 1
[tex]\[
1 + 0.04 = 1.04
\][/tex]
### Step 5: Raise this result to the power of [tex]\( 2 \cdot 10 \)[/tex]
[tex]\[
(1.04)^{20}
\][/tex]
### Step 6: Calculate the power
[tex]\[
(1.04)^{20} \approx 2.191123142
\][/tex]
### Step 7: Multiply this result by 12000
[tex]\[
12000 \times 2.191123142 \approx 26293.47771640105
\][/tex]
### Step 8: Round the result to two decimal places
[tex]\[
26293.48
\][/tex]
Therefore, the final expression evaluates to approximately [tex]\( 26293.48 \)[/tex] when rounded to two decimal places.
