The price of a European call that expires in 3 months and has a strike price of $30 is $3. The underlying stock price is $31. The stock pays no dividends. Risk-free interest rate is 10% per annum with continuous compounding.

Suppose that the price of a European put with the same maturity and strike price is $1. Describe the arbitrage opportunity and compute the arbitrage profit.

Now suppose that the stock pays a dividend of $0.50 in 2 months. Find the price of the European put (with 3-month maturity and strike price of $30 (typo corrected)) using the put-call parity with dividends.