Changing compounding frequency Using annual, semiannual, and quarterly compounding periods, $(1)$ calculate the future value if $$6,000$ is deposited initially at $11\%$ annual interest for $6$ years and $(2)$ determine the effective annual rate $($EAR$).$

Annual Compounding

$(1)$ The future value, $F{V}_n,$ is $ $($Round to the nearest cent.$)$