The spot price for gold is $1,200 and the the 6-month risk-free rate is 3% continuously compounded.

(1) Calculate the 6-month Futures price of gold.

(2) Describe a trading strategy to make arbitrage profits if the quoted futures price is $10 lower than the fair value you calculate in Part (1). Show the cash flows to each element of your trading strategy.

(3) Describe a trading strategy to make arbitrage profits if the quoted futures price is $10 more than the fair value you calculate in Part(1). Show the cash flows to each element of your trading strategy.