Show that if C is the price of an American call with exercise price K and maturity T on a stock paying a dividend yield of q, and P is the price of an American put on the same stock with the same strike price and exercise date, 

where S₀ is the stock price,  is the risk-free rate, and r > 0. To obtain the first half of the inequality, consider possible values of: 

Portfolio A; a European call option plus an amount  invested at the risk-free rate 

Portfolio B: an American put option plus e^–qT of stock with dividends being reinvested in the stock 

To obtain the second half of the inequality, consider possible values of: 

Portfolio C: an American call option plus an amount Ke ^–rT invested at the risk-free rate 

Portfolio D: a European put option plus one stock with dividends being reinvested in the stock

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