1. Suppose the current price of S&P 500 index is $3000 and the interest rate is 3%. Assume that S&P 500 does not pay any dividends. Also, suppose there is a forward contract whose underlying asset is S&P 500 index and the expiration date is 6 months from now. In this situation.

(a) What is the fair delivery price of that forward contract?

(b) Now, suppose the delivery price of the forward contract is given by $3200 instead of what you have derived above. Then, you can exploit an arbitrage opportunity as follows. You first sell the forward contract. Next, you borrow $3000 from a bank and then buy one share of the S&P 500 index. Using this strategy, how much profits can you make 6 months from now?

(c) Now, suppose the delivery price of the forward contract is given by $3010. Then, you can also exploit an arbitrage opportunity as follows. You first buy the forward contract. Next, short one share of the S&P 500 index and then deposit $3000 in your bank account. Using this strategy, how much profits can you make 6 months from now?