Question 2 :

A businessman intends to buy a bungalow and he is going to get a home loan. He can afford to make payment of RM400000 per year. The payments are distributed out and paid constantly throughout the year. The current interest rates are 2%, 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 () be the loan balance after years. State the differential equation and solve to get ().

b)The businessman plans to get a 20-year loan. How much the home loan amount (in whole number) 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 400000 at Year 5. In which year will he settle the full payment of the loan?