Evaluate the following expression for [tex]\( k = 2 \)[/tex] and [tex]\( n = 10 \)[/tex].

[tex]\[
12{,}000\left(1+\frac{0.08}{k}\right)^{kn}
\][/tex]

(Do not round until the final answer. Then round to two decimal places as needed.)



Answer :

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.