Assume that the Black-Scholes framework holds. The price of a nondividend-paying stock is $30.00. The price of a put option on this stock is $4.00.

You are given:

(i) ∆ = −0.28

(ii) Γ = 0.10 

Using the delta-gamma approximation, determine the price of the put option if the stock price changes to $31.50.

(A) $3.40

(B) $3.50

(C) $3.60

(D) $3.70

(E) $3.80