You want to buy a $$242,000$ home. You plan to pay $10\%$ as a down payment, and take out a $30$ year loan at $6\mathrm{.}25\%$ interest for the rest.

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

b$)$ What will your monthly payments be$?$

c$)$ How much total interest do you pay?

d$)$ Suppose you want to pay off the loan in $15$ years rather than $30.$ What will your monthly payment be$?$