What should the price of the european put option for 100, Financial Management

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What should the price of the european put option for 100

The current price of a stock is $47.20. One month from now, the price will either be $48 or $46.50. The nominal risk-free interest rate is 3% convertible monthly. In order that there not be an arbitrage opportunity, what should the price of the European put option for 100 shares of this stock, if it allows the holder to purchase the stock for $47 per share in one month?

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