Peter is planning to purchase a house. The mortgage interest rate is r% per year. He can afford monthly payment of k dollars. Suppose that he borrows loan of So dollars.
(a) Set up differential equation on S = S(t), the amount of money he owes after t years. Describe the initial value clearly. The equation is So(1+r) -12kt. (b) Solve the differential equation in (a). Show the details of your solution.