Consider a security that pays S(T)k at time T (k 1) where the price S(t) is governed by the standard model dS(t) = S(t)dt + S(t)dW(t). Using Black-Scholes-Merton equation, show that the price of this security at time t < T is given by c(t, S(t)) = S(0)ke(k1)(r+k 2 2)(Tt).