Spot price of gold is $$1,407\mathrm{.}40/$oz$.$ The total interest rate on three$-$month loans and deposits is $0\mathrm{.}75\%($i$.$e$.$ $$100$ borrowed today would require a payment of $$100\mathrm{.}75$ in three months$).$

a$.$ Assuming no storage cost and no transaction cost, determine the no$-$arbitrage price for a gold futures contract maturing three months from now.

b$.$ Suppose that the three$-$month gold futures contract is actually traded at $$1,420\mathrm{.}20/$oz$.$ Determine if an arbitrage opportunity is present. If so$,$ describe a trading strategy that takes advantage of this arbitrage opportunity and calculate the profit of the strategy per contract. Make sure to clearly identify what position should be taken in the futures contract, whether the asset should be bought or sold, and how much cash will have to be borrowed or invested. The contract size is $100$ oz$.$

Note. Round all results to four decimal places.