An auto repair shop borrowed $$12,000$ to be repaid by monthly payments over $5$ years. Interest on the loan is $9\%$ compounded monthly.

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

b$)$ What is the outstanding principal after payment $29?$

$($c$)$ What is the interest paid on payment $30?($d$)$

How much principal is repaid in payment $30?$