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A New York firm is offering a new financial instrument called a happy call. It has a payoff function at tim T equal to max(0.5ST,

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A New York firm is offering a new financial instrument called a happy call. It has a payoff function at tim T equal to max(0.5ST, ST K), where St is the price of a stock at time T and K is a fixed strike price. You always get something with a happ: call. Suppose that the risk free interest is 10% per year and the volatility of the stock price is 20% per annum The current stock price is $30 per share. Let K = $25. Please use the Black-Scholes formula to determine the present value of the happy call with T = 0.5

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