With United Airlines Mileage Plus Program, you can earn up to 25,000 miles for opening an account with Ameritrade. That should be enough miles for a free domestic round trip ticket. All you have to do is open and fund a TD Ameritrade account.
TD Ameritrade gives you the trading tools you need and $9.99 commissions on internet equity trades no matter how many shares you buy.
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For details, go to www.tdameritrade.com/united.