Is an American put option price same as an European one?

[timlee]

Suppose that the price of a stock is $100. A European at‐the‐money call option with a maturity of one
year hence costs $10. The risk‐free rate is 10 percent. There are no dividends.
(a) Find the price of a European at‐the‐money put option with a maturity of one year.
(b) Will the price of an American at‐the‐money put option be lower, higher or the same than the European at‐the‐money put option in (a)?

For (a) From call put parity, the price of the put option is 10+100/1.1-100 = $0.91.
I was wondering how to answer (b)? I know that with the same strike value and maturity, the prices of an American call option and an European call option are the same, Since the stock has no dividend. But for the prices of an American put option and an European put option, I am not sure.

Thanks!

 

[amir]

the price of American put option is always greater than the price of European put option