Find the compound amount for the deposit. Round to the nearest cent. $\$ 4500$ at $5.8 \%$ compounded semiannually for 6 years

Step 1 ：Given that the principal amount (P) is \$4500, the annual interest rate (r) is 5.8%, the number of times that interest is compounded per year (n) is 2 (since it's compounded semiannually), and the time the money is invested for in years (t) is 6.

Step 2 ：We can convert the annual interest rate from percentage to decimal by dividing it by 100. So, \(r = \frac{5.8}{100} = 0.058\).

Step 3 ：We can use the compound interest formula \(A = P(1 + \frac{r}{n})^{nt}\) to find the compound amount (A).

Step 4 ：Substitute the given values into the formula: \(A = 4500(1 + \frac{0.058}{2})^{2*6}\).

Step 5 ：Calculate the expression to get the compound amount: \(A = 6341.573216045244\).

Step 6 ：Round the compound amount to the nearest cent to get the final answer: \(\boxed{6341.57}\).