European Call Option Valuation using Binomial Model

XYZ Corporation is evaluating a three-step binomial model to value its European call option on its stock, which is currently priced at $100. The stock is expected to rise to $120 or fall to $80 at the end of the first period (6 months). If it rises to $120, it will either rise again to $144 or drop to $96 in the second period (the next 6 months). If it drops to $80, it can either rise to $96 or fall to $64. The risk-free rate is 5% annually.

Given this scenario, calculate the value of the European call option using the binomial model at the end of three periods, assuming the exercise price of the option is $110.