Susan Smith just arranged to purchase a $$400,000$ vacation home in Turks and Caicos. The mortgage

has a $7\mathrm{.}5\%$ APR $($Annual Percentage Rate$)$ and calls for equal monthly payments over the next $30$ years.

The first payment will be due in one month.

a$)$ What is Susan's monthly payment?

b$)$ With the terms given above, Susan makes the monthly payments for $12$ years and then she inherits a

fortune from a relative. At that point, she considers paying off the loan. How much would she pay to the

bank if she chooses to pay off the loan?

c$)$ Instead of paying off the loan after $12$ years, she can alternatively refinance the remaining balance at

a $4\mathrm{.}8\%$ APR. What would her monthly payment be if she chooses to refinance?