Compute the intrisinc values, time values, and lower bounds of the following put. Identify any profit opportunities that may exist. These as American options for purpose of determining the intrinsic value and time values and European options for the purpose of determining the lower bounds. The stock is currently worth $146.3. The discount factor are (1+r)^-T = 0.991,0.986,and 0.981 respectively.

a. t= 20 exercise price is $145 put is worth $2.10

b. T= 35 exercise is $146 put is worth $3.26

c T= 55 exercise price is $148 put is worth $5.42