Yeti You've illustrated my point very well.
The animals have another section after this - essentially the intro. So it's something like: Am C D F Am C E7 E7 / Am C D F Am E7 / Am C D F Am E7 Am E7. But many sites give something similar to what you've got (perhaps an E at the end). Listen to the Animals version. For what it's worth, I got those chords from Justin Guitar.
And it's E or E7 depending on source.