At exactly 35 year of age, with $100,000 in his savings account Alex plans to buy a house. A bank is willing to loan him the necessary funds provided that he puts up 20% of the purchase price, uses the house as the collateral and is committed to making monthly payments for the next 15 years. a) With stamp duty of 2% of the purchase price payable by the buyer, how much is the most expensive house that Alex can afford right now? Suppose the house that Alex buys is worth $420,000. He pays the stamp duty and 20% of the purchase price by himself and borrows the rest from the bank. The interest rate is fixed at 10.2% per annum compounded monthly for the first 36 months. After 36 months, interest rate is revised annually benchmarked from the central bank rate. b) The monthly payments for the first 36 months is determined based on the assumption that the interest rate is fixed at 10.2% for the full duration of the loan. Determine the monthly payment for the first 36 months. c) Calculate the outstanding balance immediately after the 36th monthly payment. After 36 months, the interest rate for the next year is revised to be 9.6% per annum (compounded monthly). The monthly payment for the next 12 months is calculated based on the assumption that the interest rate will remain fixed at 9.6% for the rest of the loan. d) Calculate the monthly payment and the outstanding balance immediately after the 48th monthly payment. Immediately after the 48th monthly payment, Alex receives an offer to buy his house at the price of $500,000. Since he has only lived at this house for 4 years, he would have to pay 10% capital gain tax on his profit. Furthermore, he would have to pay back the bank the outstanding loan with a 0.5% surcharge due to early termination of the loan agreement. e) Should Alex sell his house if he requires at least 10% return compounded monthly on his investment? f) Suppose Alex decides to sell his house. Calculate the internal rate of return of Alex's investment. Alex decides not to sell his house after all. For the next 12 months, the bank sets the interest rate to be 9.3% per annum compounded monthly. On the other hand, since his house is now worth more, he has the option of take on an additional loan of $50,000 without further collateral. g) Assume that the interest rate will remain 9.3\% forever. Determine the monthly payments Alex needs to make if he decides to take on the additional loan and if he decides not to take on the additional loan. h) Alex decides to take on the additional loan but he still wants to keep his original monthly payment as if he did not take on the additional loan. At what age will he be able to discharge the loan completely