An auto repair shop borrowed $$17,000$ to be repaid by monthly payments over $7$ years. Interest on the loan is $3\%$ compounded monthly.

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

b$)$ What is the outstanding principal after payment $35?$

c$)$ What is the interest paid on payment $36?$

d$)$ How much principal is repaid in payment $36?$