A stock index that pays no dividends is currently priced at $1,000. Assume that you can borrow at 7% and lend at 4% (continuously compounded). You are considering arbitrage opportunities for a one year forward contract in the index. a) Assuming no transaction costs, find the range of forward prices that will result in a cash-and carry arbitrage profit, and find the range of forward prices that will result in a reverse cash-and carry arbitrage profit. b) Suppose that there is a $5 cost for going either long or short on a forward contract on the index and there is a 1% cost to go short or long on the index at time 0, but the forward contract is settled by delivery of the index at time 1 with no cost. Find the upper and lower no-arbitrage bounds for the cash-and-carry and reverse cash-and-carry arbitrage.