Your parents have just purchased a town house for $$200,000$ in Catskill, NY$.$ They obtain financing with the following terms: a $20\%$ down payment and the balance to be loaned over $30$ years at $9\%$ compounded monthly.

a$)$ What is their down payment? $($hint: $20\%$ of the price of the house $$200,000)$

b$)$ What is the loan amount? $($hint: the balance after the down payment from part a$)$ above$)$

c$)$ How much is their monthly payment on the loan?

d$)$ How much total interest do they pay over the life of the loan?