1. The spot price of gold is $1,250 and the continuously compounded risk-free interest rate is 5%. Assume that gold will not have any storage cost or income.

(1) What is the futures price of gold with 12-month maturity?

(2) If the futures price is quoted at $1,320, 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.

(1) Calculate the fair price of the 1-year forward contract on the stock.

(2) If the actual forward is quoted at $152, can you identify an arbitrage opportunity? If yes, please complete all necessary transactions to realize the profit.

3. Suppose that the interest rates (continuously compounded) in the United States and Britain are 3% and 2%, respectively, and that the spot rate is S₀ = $1.30 per . How much is the 1-year forward rate?