That's the right result! And now when you change directory, the prompt will change.
PS1 is described in the man page, in this case from KSH:
PS1 The value of this variable is expanded for parameter expansion, command substitution, and arith-
metic substitution to define the primary prompt string which by default is ``$''. The character
! in the primary prompt string is replaced by the command number (see Command Re-entry below).
Two successive occurrences of ! will produce a single ! when the prompt string is printed.
Setting PS1 in this way is only temporary. Set (or modify) it in your $HOME/.profile to make it permanent, so it's there each time you log in.
There's not much to my prompt, or .profile, but I set in there:
$ cat .profile
alias ll='ls -al'
set -o vi
export EDITOR=vi
PATH=$PATH:/Users/scott/bin
PS1='$PWD $ '
Depending on your system, the default PS1 could be defined somewhere in /etc: /etc/profile, /etc/environment, /etc/bashrc, etc.