Find the future value and interest earned if $\$ 8704.56$ is invested for 8 years at $4 \%$ compounded (a) semiannually and (b) continuously.
(a) The future value when interest is compounded semiannually is approximately $\$$ (Type an integer or decimal rounded to the nearest hundredth as needed.)

Step 1 ：Given that the principal amount (P) is $8704.56, the annual interest rate (r) is 4% or 0.04, 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 8 years.

Step 2 ：We use the formula for future value when interest is compounded semiannually: \(FV = P * (1 + r/n)^{nt}\)

Step 3 ：Substitute the given values into the formula: \(FV = 8704.56 * (1 + 0.04/2)^{2*8}\)

Step 4 ：Solving the equation gives us the future value: \(FV = 11949.495537103541\)

Step 5 ：Rounding to the nearest hundredth, the future value when interest is compounded semiannually is approximately $11949.50. This is the amount of money that will be in the account after 8 years.

Step 6 ：\(\boxed{11949.50}\) is the final answer.