Question 6 In Question 5 the 30 year mortgage was $200,000 and the interest rate was 4% per year compounded daily. We modelled the change in what we owe the bank

with the differential equation M (t) = r-M(t) - P dollars per year We solved the differential equation with initial value M(0) = 200000. We worked out if we set P= $11448.10 per year then M(30) = 0. But the differential equation assumes a continuous process in which we are continually being charged interest and we are continually paying down the mortgage. In reality the bank charges us interest once a day and we make payments once every two weeks or once a month at the end of the month. Let's assume monthly payments. Assuming no leap years for simplicity, over a 30 year period there will be 30-365 = 10,950 interest charges which is almost continuous. But there are only 30-12 = 360 payments, less continous.