1. Tan Yoon has agreed to sell 50 shares of a stock to his brother in two months for $2,500, if his brother so desires. The current price of the shares is $2,430, and each month that price will either go up by 8% or down by 5%, independent of what happens in the other month. If the price ends up going up each month, then Tans brother will accept the offer and Tan will receive only $2,500 for an asset worth $2,834.35. Otherwise, the stocks will have a market price of less than $2,500, so Tans brother will not accept the offer to buy the stock from Tan.

   Suppose that Tan Yoon notes that he could purchase a call option having as underlier 100 shares of the same stock, expiration in two months, and strike price $5,000, and that it has a non-arbitrage price X, based on a risk-free annual effective interest rate of 5%. Find X.