3. (15 points) Consider a one-year futures contract on gold. We assume that it costs $2 per ounce per year to store gold, with the payment being made at the end of the year. The spot price is $1600 per ounce and the risk-free rate is 5% per annum for all maturities. Note: For this question, we assume that the underlying asset of each gold futures contract is ONE ounce of gold. (1) What is the present value of the storage cost? (2) What is the theoretical futures price? (3) Suppose the actual gold futures price is $1700. What strategy should an arbitrageur implement in order to take advantage of this opportunity, and how much is the profit? Use the following table to show your positions (in the futures contract, the underlying asset and cash account) on date t (today) and the expiration day T. Assume that the spot price of gold on the expiration day T is $1800. Action Cash Flow at t Cash Flow at T 1. (hint: borrow or lend?) 2. (hint: buy or sell Gold?) 3. (hint: long or short futures?) 4. (hint: storage cost) Total