1. The spot price of gold is $1,800 and the continuously compounded risk-free interest rate is 3%. Assume that gold will not have any storage cost. Please answer the following three questions: (1) How much is the futures price of gold with 12-month maturity? (2) If the actual futures price is quoted at $1,875, how can you make money through arbitrage? Please show all transactions. (3) If the futures price is quoted at $1,845, how can you make money through arbitrage? Please show all transactions. 2. Consider a 1-year forward contract on the IBM stock. Currently the stock is trading at $150 per share on the NYSE. The stock is expected to pay a cash dividend of $5 per share in six months. The continuously compounded interest rates are 5% for six months and 6% for 12 months. Please calculate the fair price of the 1-year forward contract on the stock. 3. Consider a six-month futures contract on the S\&P 500 index. Suppose that the 500 stocks underlying the index provide a dividend yield of 2% per annum, that the current level of the index is 4,000 , and that the continuously compounded interest rate is 4% per annum. Please calculate the fair price of the 6-month futures contract. 4. Some time ago, you entered a forward contract to sell gold at K=$1950. Today, the forvard contract has one year remaining to maturity. The current spot price of gold is $1900 oz and the risk-ftee interest rate is 5% (continuously compounded). Please calculate the value of this forward contract