Hi Virginia,
Standard Fields are not editable, as such, if they were not designed to only be updated by Finance it won't help.
Two workaround I can offer:
Create a Custom Field which is updateable only by Financial which gets the value from that Field and hide the Standard Field
Hide the Standard Field and create a special View for the Financial User
In general, please touch-base with your CSM (Alex Gorman I believe), so he can tell you about Profiles which are coming soon, which I believe will help you realise this setting with no needed workarounds.