There is a European call and a European put on AAPL (will not pay dividends in the near future) with the same exercise price and the same time to maturity. Assume the current stock price is $110, the exercise price is $120, the time to maturity is 9-month, the risk- free rate is 3% and the standard deviation of AAPL's return is 30%. 

a. Based on Black-Scholes formula, what is the call price and the put price? 

b. Assume the risk-free rate might change from 0.25% to 5%, with a step size of 0.50%. What are the respective call and put prices? Plot them on a chart with y- axis as option price and x-axis as risk-free rate. If the risk-free rate increases, will the option prices (call and put) increase or decrease? 

c. Assume the stock price might change from $60 to $150, with a step size of $5, produce a chart comparing the put's intrinsic value [=max(X-S,0)] and its Black- Scholes price.