Suppose that you observe that an index with no dividends has spot price $1,100, and the risk\ free rate is 5%. A 3-month American call option with strike $1,080 has a price of $52. Determine\ a lower bound for the price of an at-the-money American call option. Determine a lower bound\ for the price of a 3-month American put option with strike $1,080.\ 1