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PREVIOUS EXAM : a. Consider a two-period consumption model consisting of now, t = 0, and next year, t = 1. There are two investors, Investor A who is patient and wants to wait and consume the maximum amount possible at t = 1, and Investor B who is impatient and wants to consume the...

PREVIOUS EXAM : a. Consider a two-period consumption model consisting of now, t = 0, and next year, t = 1. There are two investors, Investor A who is patient and wants to wait and consume the maximum amount possible at t = 1, and Investor B who is impatient and wants to consume the maximum amount possible now. Both investors have an income of \$200,000 today and no income at t = 1. Both investors have access to a real investment opportunity costing \$200,000 now and returning a guaranteed \$215,000 at t = 1. They also have access to risk-free borrowing and lending at an annual rate of 10%. Explain the investment decisions taken by each investor (both real and financial) and the resultant cash flows and consumption, including a brief discussion of the optimality of the net present value (NPV) rule. b. You have just purchased a house in Sydney for \$2 million, using your own savings to make a down payment equal to 20% of the house's value, with the remainder financed via a 25-year mortgage. The mortgage has fixed monthly payments, with the first payment due in exactly one month. The stated annual interest rate on the loan is 6% with monthly compounding. How much of the loan principal will you repay in the first year of the loan, expressed as a percentage of your total annual mortgage payment. Will this percentage increase, decrease, or stay the same in subsequent years? Explain.