You have $\$ 10,000$ to invest. One bank pays $0.8 \%$ interest compounded semiannually and a second bank pays $0.36 \%$ interest compounded monthly. Complete parts a and $b$. a. Use the formula for compound interest to write a function for the balance in each bank at any time $t$ Write a function for the balance in the first bank with interest compounded semiannually at any time $t$. \[ A=\square \] (Simplify your answer. Use integers or decimals for any numbers in the expression. Do not include the $\$$ symbol in your answer.)

Step 1 ：The formula for compound interest is \(A = P(1 + r/n)^{nt}\), 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, \(P = \$10,000\), \(r = 0.8\% = 0.008\), \(n = 2\) (since interest is compounded semiannually), and \(t\) is the variable we're solving for.

Step 3 ：So, we need to write a function that calculates \(A\) given \(t\) using these values.

Step 4 ：The function for the balance in the first bank with interest compounded semiannually at any time \(t\) is \(\boxed{A=10000 \left(1+\frac{0.008}{2}\right)^{2t}}\)