I have used the following without success. The active workbook closes, indeed, but the excel window remains open.
Application.ActiveWindow.Close SaveChanges:
To avoid the Save prompt message, you have to insert those lines
Application.DisplayAlerts = False
ThisWorkbook.Save
Application.DisplayAlerts = True
After saving your work, you need to use this line to quit the Excel application
Application.Quit
Don't just simply put those line in Private Sub Workbook_Open() unless you got do a correct condition checking, else you may spoil your excel file.
For safety purpose, please create a module to run it. The following are the codes that i put:
Sub testSave()
Application.DisplayAlerts = False
ThisWorkbook.Save
Application.DisplayAlerts = True
Application.Quit
End Sub
Hope it help you solve the problem.