The price of a house is $500; 000. $100; 000 is your down payment while you borrow the other $400; 000 amortized at a 6% annual rate compounded monthly.

(a) Find the monthly payment for the loan. After 30 years, how much will you have paid for the house?

(b) After 10 years, what percentage of the total loan have you paid?

(c) If you make double payments from the beginning, how much time is saved? How much interest is saved?