The price of a home is $250; 000. $50; 000 is your down payment while you borrow the other $200; 000. Assume a 5% annual rate compounded monthly.

(a) Find the difference in total interest paid for 30 year and 15 year amortization schedules.

(b) Seven years after starting the 30 year loan, you decide to re-finance the remaining balance of the loan at 4:2% for 15 years. In addition, you pay an extra $100 on your monthly payment. What is the total amount you pay for the house after the loans are paid?