Question 3 a. Suppose the price of a mortgage that you are interested in buying is 300,000 and you have 10% of the money for down payment handy. The bank will loan you the remaining 90% with an annual interest rate of 7.5% for a 35-year term. Find your monthly payment. [6 marks] b. You are discussing a loan deal with a lender. You want to borrow 45,600 for one year. The interest rate is 16 per cent. You and the lender agree that the interest on the loan will be 0.16 ~ 45,600 = 7,296. The lender deducts this interest amount from the loan up front and gives you what is left. What is the correct interest rate to pay on the amount, assuming that all the other information in the question is correct? [4 marks] c. You just attended a workshop organised by Warren Buffet, a business tycoon and considered one of the most successful stock market investors. He lectured you on how to play in the stock market and make millions. You decide that you want to become a millionaire by the time you are 45. You now believe that you can beat the market and can earn about 14.1 per cent per annum from investing in equities. You have just turned 21 and you decide to play the stock market. How much do you need to invest quarterly to achieve your goal of 10,000,000? [7 marks] d. If you increase the number of payments on an amortized loan, does the payment increase or decrease? Why or why not? [5 marks] e. What effect on the present value of an annuity does increasing the interest rate have? Does a change from 7% to 5% have the same dollar impact as a change from 5% to 3%? Explain with example. (ii)