European Call Option Valuation with Binomial Model

Consider a European call option on a stock that is currently priced at $50. The option has a strike price of $55 and matures in one year. Using a one-period binomial model, the stock can either move up by 20% or down by 10% over the year. Assume the risk-free interest rate is 5%. Calculate the price of the call option using the binomial model and determine the correct risk-neutral probability (p) for the stock moving up.

Following the one-period binomial method, calculate the option's intrinsic and expected final payoffs to arrive at the call option price.