Take $K=50, S=$52, the values of u=1.05 , d=0.95 , no dividends, r-hat = gross interest factor = 1.025 per binomial period as given - and compute

a) the VALUE of the American Put today if the Option had 1 period to go

b) Its value as an American put with 2 periods to go.

c) Its value as a EUROPEAN put with 2 periods to go. What is the premium of the Amput over its European counterpart?

d) repeat all of the above, a, b, and c, but for American calls