The payoff of a capitalized-strike American put option is (left(K e^{r t}-S_{t} ight)^{+})if exercised at time (t).

The payoff of a capitalized-strike American put option is \(\left(K e^{r t}-S_{t}\right)^{+}\)if exercised at time \(t\). Prove that the price of this option is the price of a European put, with strike \(e^{r T} K\).