These days, it's recommended to not use Vector. Use a different type of list, like ArrayList, instead.
If you're curious for the reasoning behind this, I'd recommend a quick search on this forum for "vector arraylist" in the subject. (Note that the search page link is at the top right of this page.) Also, you might like to read
the JavaWorld Java Q&A on the subject.
Even if yours is a learning exercise, you might as well learn to use the preferred APIs, while doing it.
Concerning this line of code:
vctAcct.add( new String (acctName) ); Is
acctName a String? If so, why are you creating a new String with a String? Are you familiar with what the difference between the following two lines of code are?
String string1 = "myString";
String string2 = new String("myString");
On the issue of sorting, forgetting about the JTable for a moment, have you tried just iterating through the collection, after sorting it, and simply printing it out to the console to see if it got sorted correctly?