Binomial Call Option Pricing

Consider a European call option on a stock currently priced at $50. The stock can either increase by 20% or decrease by 10% over the next period, leading to an up state of $60 (50 + 50*0.20) and a down state of $45 (50 - 50*0.10). The risk-free rate is 5% per period. Using a one-period binomial model, calculate the theoretical price of the call option.

After calculating the value of the call option, consider how the introduction of a risk-neutral probability affects the valuation. What is the price of the call option derived from the binomial model?