|IMHO, you are taking unnecessary risks storing any passswords for banking or stock sites. I would carry it further and state you shouldn't keep anything on your hard drive that you wouldn't want a stranger to access.|
That is what CDR/CVDR, flash drives, external drives that you disconnect, etc, are for.
I trade on Scottrade and you CAN'T save the password for your account.
Out of curiosity, WHY did you have to change your log-in at the bank?