I haven't done any Android development yet, but won't the app close when all activities are closed? IF so, all you need to do to close the app immediately is finish all activities, not just the current one. If the existing activities are not retrievable using the API then just store them all yourself.
It depends on how the application is structured. An Android app can contain components other than activities (like services, wallpapers, content providers, broadcast receivers). Some of those might still be running even if all activities have been terminated. If the app consists only of activities, then terminating those will leave no part of the app running.