Suppose ST is the price at time T of a stock that pays no dividends and follows geometric Brownian motion. An exotic derivative on the stock has a guaranteed payoff at time T, and no other payoff at any other time. The price of the derivative at time t T is S e^( 1/8^2+ 1/2r)(tT) , where S is the stock price at time t. (i) If the stock price at time T is $25, what is the option payoff? (ii) Show that the price function satisfies the BSM differential equation.