Let S(t) be the time-t price of a nondividend-paying stock. The expected appreciation rate is 10%, and the volatility is 30%. The current stock price is 20. (a) Find the equal-tailed 90% lognormal prediction interval for S(2). (b) Using Excel Solver, find the shortest 90% prediction interval for S(2). Consider a 1-year 25-strike asset-of-nothing put on the stock. (c) Calculate the probability that the put would be in the money after 1 year. (d) Find the 20th and 80th percentile of the payoff. (e) Find the expected payoff.