A debt of $$36,000$ is repaid over $13$ years with payments occurring monthly. Interest is $12\%$ compounded

semi$-$annually.

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

$($b$)$ What is the outstanding principal after payment $63?$

$($c$)$ What is the interest paid on payment $64?$

$($d$)$ How much principal is repaid in payment $64?$