You have to specify that you want the terminal that you initiate to perform your actions:
xterm -e "echo -n a new terminal && /bin/sh"
Would start a new xterm window, say "a new terminal," and then not exit but start the shell. the -e option tells it to run the following set of code. If you don't put the "&& /bin/sh" at the end of the code, the window will close. You could also use the -hold option to keep the window open, but without the directive to start a shell it'll be a useless window.
Regardless, the -e option has to be the very end of the command.
Hope this helps some. Btw I don't know why you use the -n option--all that does is not start a new line after echoing "a new terminal" doesn't it?