App delivery is done by Google using a combination of their Internet servers and the Google Play app.
This error (RPC:S-7:AEC-0) indicates a problem between the Google Play app on your Android device and the Google Play Servers that deliver the apps to your Android device – we’re not directly involved and unfortunately therefore cannot "fix" this issue for you.
A google for this error yields many people reporting similar problems, though nothing dated recently.
The consensus is that it is a problem between the Google Account used by the phone and the Google Play web servers getting out of sync.
Contact Google (via the “Contact us” link on this page) for more information. You could try this page and follow the suggestions by clicking each suggestion in turn.