"I will boil you a potato."
Translation:감자를 삶아줄 거야.
The word 주다 means to give. So, when you add it to the end of a conjugated verb, you're giving the impression that you're doing something for the sake of the object of the sentence. It also gives a bit of a nuance that you're saying 'please' or 'for something/someone'.
나의 아내 살려주세요!
Please save my wife (for me)!
저 사람은 그 사람 살렸어요.
That person over there saved that person.
Please buy this (for me)!
I love whoever took the time to create these lessons, but they need a major edit. 뭐뭐할거야 is less like "I will" and more like "I am going to." This seems trivial but it isn't. The 할거야 is generally used to signify something decided in advance. 'Will' is generally indicated with "할께" and is often done in the moment, showing eagerness or at least willingness.
"I shall" is not representative of modern English.
So, almost. But, slightly differnet. 할께요 is expressive of a determined effort to undertake an action, but not an "I'm going to." Like, if whoever you are with says, "요리 시작!" and you say "아냐 내가 할께", this means, "starting the cooking!," and then,"no no, I'll do the cooking." So it's much more immediate than "I'm going to." It's a pretty strict WILL do something.
-ㄹ것이다, -ㄹ거예요 (please note the spelling - it's not -거에요, but -거예요) is more a general plan. So, something you plan to do, but are not necessarily suddenly determined to do suddenly in the moment. It's less dynamic and less forward-thinking.
So: 제가 할거예요. I'm going to do it. (A plan for an action coming up soon, but not necessarily immediately).
제가 할께요. "I'll do it." (Immediate volition, taking responsibility away from another person, sometimes to be kind/accomdating, etc.)