SP500 index is trading at 2800. Binary call option will pay you $1 if the price at expiration is above the strike price $0 otherwise. Binary put will pay 100 if price at expiration is below the strike and 0 otherwise.

a) You believe in the next year, the price will follow a normal distribution with mean at current price and standard deviation at 20% or 2000 *20% = 400 points

What is the price of a binary call option with strike at 2500

b) Binary PUT with strike at 2400 with 1 year before expiration is priced at 10. What is implied annual volatility