Question 5

Let M(t) be the amount owed on a 30 year mortgage of $200,000 at time t years.

Suppose the annual interest rate on the mortgage is 7=4%.

Suppose the term of the mortgage is 30 years, i.e., M(30) should be 0.

Suppose we pay $P per year.

We can model the change in what we owe the bank with the differential equation

M (t) = r.M(t) - P dollars per year

and initial values M(0) =$200000.

This model assumes the interest is charged continuously (banks usually charge interest daily which is

approximately continuous) and if we assume we make the payments continuously (banks usually

require us to pay monthly or weekly which is approximately continuous over 30 years). So the values

we obtain with it will be approximations.