Consider a European-style option on a non-dividend-paying stock share, whose price follows a geometric Brownian motion with drift 5% and volatility 35% (per year); the continuously compounded risk-free rate is 3%; the option matures in 4 months, and the current underlying asset price is \($50.\) The payoff (in USD) is given by the following contingency table depending on the terminal price of the underlying asset:

Find the option price.

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Payoff 0 Condition ST 50 50 ST < 60 60 ST <70 70 ST 5 10 10 1