KGYSAK - 게 vs 께

What in the world is the difference between 그렇게 할께요 and 그렇게 할게요? Anytime I see 할께요 and 할게요 I just get frustrated not knowing which one is which. I learned 을 게요 of course but I very often see 을 께요 which one is right? Is one different from the other?

After asking countless number of people this question and never getting a straight or consistent answer, I was starting to lose hope. Thankfully, my teacher finally clarified. There are indeed the same thing. Both imply future intent but only one is spelled correctly. ㄹ께요 is just a cute or common mispelling that sticks.....kind of like "light" and "lite" to describe a food's sugar or calorie count. We know "lite" is wrong but accept it anyway.

I have actually heard that the prior to 1988 it was officially spelt as 께 but I can't verify that. Either way, it is currently spelled as 게.

Scratch that one off the list.