Use DerivaGem to calculate the value of an American put option on a nondividend paying stock when the stock price is $30, the strike price is $32, the risk-free rate is 5%, the volatility is 30%, and the time to maturity is 1.5 years. (Choose Binomial American for the option type and 50 time steps.) a. What is the options intrinsic value? b. What is the options time value? c. What would a time value of zero indicate? What is the value of an option with zero time value? d. Using a trial and error approach calculate how low the stock price would have to be for the time value of the option to be zero. e. How do the values in a. and b. change when volatility increases to 50%? Falls to 10%? Why do the values change with volatility?