You want to buy a $$252,000$ home. You plan to pay $5\%$ as a down payment, and take out a $30$ year loan for the rest.

a$)$ How much is the loan amount going to be$?$

b$)$ What will your monthly payments be if the interest rate is $6\%?$

c$)$ What will your monthly payments be if the interest rate is $7\%?$