An investor is analyzing an American call option and an American put option on a dividend-paying stock. Both options have a strike price of $20 and an expiration date in 3 months. The risk-free interest rate is 10% per year (with continuous compounding), the current stock price is $19, and a $1 dividend is expected in one month.

a) Find lower and upper bounds for the price* of the American call option.

b) Find lower and upper bounds for the price* of the American put option

* both price are at time 0