Sure, let's break it down step by step:
Given:
- [tex]\( P = 3000 \)[/tex]
- [tex]\( r = 8\% = \frac{8}{100} = 0.08 \)[/tex]
- [tex]\( k = 4 \)[/tex]
- [tex]\( n = 13 \)[/tex]
We need to evaluate the expression:
[tex]\[ P\left(1+\frac{r}{k}\right)^{k n} \][/tex]
First, calculate the value inside the parentheses:
[tex]\[ \frac{r}{k} = \frac{0.08}{4} = 0.02 \][/tex]
Next, add 1 to this value:
[tex]\[ 1 + \frac{r}{k} = 1 + 0.02 = 1.02 \][/tex]
Now, we need to raise this result to the power of [tex]\( k \times n \)[/tex]:
[tex]\[ k \times n = 4 \times 13 = 52 \][/tex]
So, we need to calculate:
[tex]\[ (1.02)^{52} \][/tex]
Next, multiply this result by [tex]\( P \)[/tex]:
[tex]\[ 3000 \times (1.02)^{52} \][/tex]
Evaluating this expression:
[tex]\[ 3000 \times (1.02)^{52} \approx 8400.984556344545 \][/tex]
Finally, rounding this value to two decimal places:
[tex]\[ \approx 8400.98 \][/tex]
So, the final answer is [tex]\( 8400.98 \)[/tex].
