Question 3 (Total 25 marks)

In 20 years you will retire and you are planning to buy a house. The house you have targeted costs $5,000,000 today and is expected to increase in value each year at a rate of 2%.

a) Calculate the price of the house 20 years later. (4 marks)

b) Assume that you can earn 5% annually on your investment. If you want to invest a single lump-sum of money now for the payment of your house 20 years later, how much you must invest now? (5 marks)

c) If you can invest at the end of each of the next 20 years, how much you must save up at the end of each quarter in order to be able to buy the house? Assume the return rate of your investment is 12% p.a. (8 marks)

d) Suppose you want to buy the house right now, and you want to borrow $3,500,000 for 20 years repayment. Assume interest rate is 12% per annum. How much you need to pay each month for returning the loan? (8 marks)