Consider a call option with strike K and maturity T, on a lognormally distributed underlying asset with spot price S, volatility , and paying dividends continuously at rate q. Assume that the risk-free interest rates are constant equal to r. (i) Finding the value of the strike price such that the of the call is 0.5 requires solving (C)=eqTN(d1)=21 for K, where N(x) be the cumulative density of the standard normal variable and d1=Tln(KS)+(rq+22)T. Write down the Newton's method recursion for solving (??) for K. (ii) Consider a lognormally distributed asset with spot price $30, volatility 30%, and paying 1% dividends continuously. Assume that the risk-free interest rates are constant equal to 2.5%. Find the strike at which the of a three months call on this asset is 0.5 . Start with 1 an ATM strike and use Newton's method with tol=106. Report all intermediate values from Newton's method