Find the compound amount for the deposit. Round to the nearest cent. $\mathrm{\$}4500$ at $5.8\mathrm{\%}$ 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: $A=4500(1+\frac{0.058}{2}{)}^{2\ast 6}$.

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: $\boxed{{\displaystyle 6341.57}}$.