A debt of $$43,000$ is repaid over $11$ years with payments occurring semi$-$annually. Interest is $10\%$ compounded annually.

$($a$)$ What is the size of the periodic payment?

$($b$)$ What is the outstanding principal after payment $11?$

$($c$)$ What is the interest paid on payment $12?$

$($d$)$ How much principal is repaid in payment $12?$

$($a$)$ The size of the periodic payment is $

$($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.$)$