Consider the E-mini S&P 500 Futures contracts traded on the CME Group. The contract specifications stipulate:

Contract Unit: $50 x S&P 500 Index

Settlement Method: Financially Settled

Additional information:

S&P 500 index today is $3,512.

March 2021 futures price (5 months from now) is $3,550.

No need to count days, just use 5 months to expiration.

You have a long position for one futures contract that you entered 1 month ago. The strike price of this contract is $3,100.

1. What is the short-term interest rate implied by the above information?
2. Compute the current value of your futures contract position.
3. How would you close your position, and how much would you have to pay or receive to do so?
4. Plot the profit and loss diagram for your contract as a function of the S&P 500 index level at expiration. Be sure to label all axes and identify the index level at which the contract value is zero.
5. Assuming you have $1,000,000 investment in the S&P 500 that you cannot trade. How many futures contracts do you need to hedge your investment (round to the nearest number)? Do you need to enter a long or a short position?