You want to buy a $$233,000$ home. You plan to pay $20\%$ 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 $5\%?$

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