You want to buy a $$204,000$ home. You plan to pay $15\%$ as a down payment, and take out a $30$ year loan for the rest.

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

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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 $6\%?$