Suppose that S = $50, K = $45, = 30%, r = 8%, and T = 1. The stock will pay a discrete $4

Suppose that S = $50, K = $45, σ = 30%, r = 8%, and T = 1. The stock will pay a discrete $4 dividend 4 months from now. Assume that the dividend is paid right before reaching the node. Compute the price of European and American put options using a three-step binomial tree.