How remove specific extension from files in one folder at once in terminal

I have a couple of files with ".old" extension.

How can I remove the ".old" extension without remove the file?

I can do it manually but with more work:

mv file1.key.old file1.key
mv file2.pub.old file2.pub
mv file3.jpg.old file3.jpg
mv file4.jpg.old file4.jpg

(etc...)

The command will work with other extensions too?

example:

mv file1.MOV.mov file1.MOV
mv file2.MOV.mov file2.MOV
mv file3.MOV.mov file3.MOV

(etc...)

or better:

mv file1.MOV.mov file1.mov
mv file2.MOV.mov file2.mov
mv file3.MOV.mov file3.mov

(etc...)