Consider an American call option with 1 year to maturity and a strike price of $50. The risk-free rate is 5% per annum. The stock is non-dividend paying, currently trading at $45, and has per annum volatility of 25%. State the absolute difference between the European Black-Scholes call option price and the American binomial price assuming:

a. 1 time step

b. 5 time steps

c. 10 time steps

d. 25 time steps

e. 50 time steps

f. 100 time steps

g. Does this agree with the intuition that it is never optimal to exercise an American call option on a non-dividend paying stock early?