A debt of $$30,000$ is repaid over $8$ years with payments

occurring monthly. Interest is $4\%$ compounded semi annually.

$-$

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

$($b$)$ What is the outstanding principal after payment $50?$

$($c$)$ What is the interest paid on payment $51?$

$($d$)$ How much principal is repaid in payment $51?$