We’ll be taking about the future tense today. Let’s look at the first sentence:

공부할 겁니다 = I will study.

The construction ~을/를 겁니다 is what makes this future tense.

지금 먹을 겁니다 = I will eat now.

This is the same construction as before, but slightly different. Here 을 겁니다 was used. When the 다 in 먹다 (to eat) is dropped, 먹 ends in a consonant. Therefore, when the stem ends in a consonant, 을 겁니다 is used. Conversely, when the 다 is dropped in 하다 (to do) 하 is the stem, which ends in a vowel. Therefore, 할 겁니다 is used.

Now let’s look at this sentence:

공부 안 할 겁니다 = I will not study.

지금 안 먹을 겁니다 = I will not eat now.

Both of these sentences has the construction ~안 를/을 겁니다.

Now compare this with these sentences:

공부 하지 않을 겁니다 = I will not study.

지금 먹지 않을 겁니다 = I will not eat.

But of these sentences have the ~지 않을 겁니다 construction. The difference between ~지 않을 겁니다 and ~안 를/을 겁니다 is that ~안 를/을 겁니다 is more colloquial and used in spoken speech, while ~지 안을 겁니다 is more formal and used in written speech. Both ~지 않을 겁니다 and ~안 를/을 겁니다 are both formal, but ~지 않을 겁니다 is slightly more formal.

Here’s also another tip, 안 and 않 are pronounced the same way. 않다 is actually a contracted form of 안 하다. Think of it as this way:

빨래하지 않을 겁니다 = I will not do the laundry.

빨래 안 할 겁니다 = I will not do the laundry.

Both sentences mean the same thing, but notice that the second sentence has the contracted form. In the second sentence, the ㅎ in 할 has moved to the bottom of 않을 of the first sentence.