-ㄹ 거예요 = most neutral way for future tense, many people write 거에요 but that's a very ugly mistake, please try not to be among those people. -ㄹ게요 = used when you do a favor for someone. 제가 해 줄게요. I will do it for you. -겠- = shows volition/determination. 나는 가수가 되겠어. I will become a singer.

할게요: -ㄹ게 is a sentence ending expressing a (light) intention and promise. 하겠어요: -겠다 (root form) is a verb conjugation expressing an intention. 할 거예요: = -ㄹ 거예요 expresses a future tense of an action or a guess, conjecture. - 거예요 is a contraction of 것이에요. - 거에요 is a misspelling of 거예요 - a common mistake even among native speakers. ex) 1.앞으로는 잘할게요: I will do good from now on. (a promise) 2.앞으로는 잘하겠어요: I will do good from now on (a statement of intention) 3.그 애는 앞으로는 잘할 거예요: He will do good from now on (a future tense) -ㄹ and -겠어 are mostly used in first person speech as they express intentions. Their meanings are often close too. -거예요 can be used for any person.