Please make sure calculations are performed correctly.

3) On November 82023 , the S\&P 500 index is at 1,300, the continuously compounded dividend yield is 3% p.a, and the continuously compounded risk-free rate is 5.2% p.a. Assume the transaction cost is zero. (3 Marks). a. What is the theoretical futures price for a December contract that expires on 18th December 2023? b. If on November 82023 , the futures contract is priced at 1,320 , is there any arbitrage opportunity? If yes, show the overall profit from this opportunity assuming that the arbitrage transaction will be executed by borrowing $20 million, the multiplier of S\&P is 250, and the S\&P index stood at 1340 on December 18