Interest is compounded semiannually. Find the amount in the account after the given time.
\begin{tabular}{ccc}
Principal & Rate & Time \\
$\$ 3000$ & $7 \%$ & 1 year
\end{tabular}
The amount in the account is $\$$
(Simplify your answer. Type a whole number or a decimal. Round to the nearest cent if needec

Step 1 ：The problem is asking for the final amount in an account after a certain period of time, given a principal amount, an interest rate, and a compounding period. The formula for compound interest is: \(A = P(1 + \frac{r}{n})^{nt}\) where: \(A\) is the amount of money accumulated after \(n\) years, including interest, \(P\) is the principal amount (the initial amount of money), \(r\) is the annual interest rate (in decimal), \(n\) is the number of times that interest is compounded per year, and \(t\) is the time the money is invested for in years.

Step 2 ：In this case, the principal \(P\) is $3000, the annual interest rate \(r\) is 7% or 0.07 in decimal, the number of times interest is compounded per year \(n\) is 2 (since it's semiannually), and the time \(t\) is 1 year.

Step 3 ：We can substitute these values into the formula and calculate the final amount.

Step 4 ：\(P = 3000\)

Step 5 ：\(r = 0.07\)

Step 6 ：\(n = 2\)

Step 7 ：\(t = 1\)

Step 8 ：\(A = P(1 + \frac{r}{n})^{nt} = 3000(1 + \frac{0.07}{2})^{2*1} = 3213.6749999999997\)

Step 9 ：Final Answer: The amount in the account after 1 year is \(\boxed{\$3213.67}\)