Changing compounding frequency Using annual, semiannual, and quarterly compounding periods, $(1)$ calculate the future value if $$6,000$ is deposited initially at $12\%$ annual interest for $5$ years, and $(2)$ determine the effective annual rate $(EAR).$

Annual Compounding

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

$(2)$ If the $12\%$ annual nominal rate is compounded annually, the EAR is $\%.($Round to two decimal places.$)$

Semiannual Compounding

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

$(2)$ If the $12\%$ annual nominal rate is compounded semiannually, the EAR is $\%.($Round to two decimal places.$)$

Quarterly Compounding

$(1)$ The future value, $F{V}_n,$ is $

$($Round to the nearest cent.$)$

$(2)$ If the $12\%$ annual nominal rate is compounded quarterly, the EAR is $\%.($Round to two decimal places.$)$