Consider a 6-month bull call spread on AAPL with strikes of $150 and $180. AAPL spot price is $165 and its volatility is 20%. The risk-free rate is 4% per annum continuously compounded. We assume that AAPL is not expected to pay any dividend.

(a) Use a 6-step binomial tree to price the spread (note: up and down movements need to match the volatility. Show all the tree parameters).

(b) What is the break-even point(s), the maximum profit and maximum loss for this strategy?

(c) Without using the binomial tree, what is the premium of the bear put spread with the same strike prices?