Suppose Ms. Lee is buying a new house and must borrow $150,000. She wants a 30-year mort...

Suppose Ms. Lee is buying a new house and must borrow $150,000. She wants a 30-year mortgage and she has two choices. She can either borrow money at 7% per year with no points, or she can borrow the money at 6.5% per year with a charge of 3 points. (A "point!' is a fee of 1% of the loan amount that the borrower pays the lender A the beginning of the loan. For example, a mortgage with 3 points requires Ms. Lee to pay $4,500 extra to get the loan.) As an approximation, we assume that interest is compounded and payments are made continuously. Let

M(t) = amount owed at time t (measured in years),

r = annual interest rate, and

p = annual payment.

Then the model for (the amount owed is

(a) How much does Ms. Lee pay in each case?

(b) Which is a better deal over the entire time of the loan (assuming Ms. Lee does not invest the money she would have paid in points)?

(c) If Ms. Lee can invest the $4,500 she would have paid in points for the second mortgage at 5% compounded continuously, which is the better deal?