A businessman intends to buy a bungalow, and he is going to get a home loan. He can afford to make a payment of RM p hundred thousand per year. The payments are distributed and paid constantly throughout the year. The current interest rates are q%, compounded continuously. Assume that the rate due to interest is proportional to the balance, and the payments are removed from the balance at a constant rate.
a) Let y(t) be the loan balance after t years. State the differential equation and solve to get y(t).
b) The businessman plans to get a 20-year loan. How much is the home loan amount (in whole numbers) that he can obtain from the bank?
c) Assuming the interest rate is fixed throughout the loan period, the businessman decided to make an advance payment of RM r hundred thousand at Year 5. In which year will he settle the full payment of the loan? r=6, so RM600,000.