You want to buy a $$238,000$ home. You plan to pay $5\%$ as a down payment, and take out a $30$ year loan at $5\mathrm{.}5\%$ 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$?$

e$)$ How much money in interest will you save if you finance for $15$ years instead of $30$ years?