Consider a European put option with exercise price is $35 and time to maturity of 3 months. The underlying asset of the option is a non-dividend-paying stock that is currently trading at $36. This stock has a historical volatility of 30% per year. Continuously compounded risk-free interest rate is 3.5%

1. Find the value of a put option at the strike price of $35 using the Black-Scholes option pricing model. Show all steps. (7 points)
2. Find the value of Delta for this option. (3 points)
3. Using just delta, what should be the change in the price of the put option if the price of the underlying stock decreases by $0.50? (4 points)
4. What is the change in the value of the put option if time changes by 1 day while all other variables remain the same in the Black-Scholes Option pricing model? (6 points)