The price of a traded security follows a geometric Brownian motion with drift μ = 0.08 and volatility σ = 0.5. Its current price is 50. A brokerage firm is offering, at cost C, an investment that will pay 100 at the end of 1 year either if the price of the security at 6 months is at least 54 or if the price of the security at 1 year is at least 10 percent above its price at 6 months. That is, the payoff occurs if either S(0.5) > 54 or S(1) > 1.10S(0.5). The continuously compounded interest rate is 0.06. If the investment is not to give rise to an arbitrage, what is C?