Mr$.$ Cillian Phoebe gets a $$12,000$ bank loan which has an interest rate of $7\%$ compounded annually and calls for six equal annual payments $($first payment one year from now$).$

$1)$ How large must each annual payment be$?$

$2)$ How much interest is paid in the second year?

$3)$ What is the ending balance at the end of the second year?

$4)$ Now assume that together with the last annual payment Mr$.$ Phoebe will make a balloon payment of $$2,000.$ Given the balloon payment, how large must each annual payment be$?$