Which is correct: 'leaving at...' or 'leaving by...', '..end of this week'?

My understanding of correct usage is 'leaving by end of this week', and that is what I have been using all along.

However looking at an example of 'informal letter', at an IELTS preparation site, I find the use of the 'leaving at...' expression. And this the the source of my confusion.

They mean different things.

"I will leave by the end of the week" means you will leave at sometime before the end of the week . . . maybe tomorrow (Wednesday), maybe Friday, but definitely by the end of the week.

"I will leave at the end of the week" is more precise and means you will not leave before the end of the week, but will leave at the end (on Saturday, for instance).