I'm considering writing the following in an email to a friend.
I'm sure the exam'll be easy.
But it just sounds wrong to me, even in an informal setting....
People do speak like this. How you wrote it is correctly spelled.
It's helpful to put this in the same category as slang - you do not want to write it this way in professional or formal writing.
An author of in a book of fiction (or a comic book)P may do this, where the author is writing how people talk, but you wouldn't see this outside of that context normally.