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.