In fact, we say "알았어" when I understood what you said and agree. A: 3시에 만나자 (Let's see at 3 o'clock) B: 알았어 (I understood and agree to see you at 3 o'clock) In this case, if B answers "알아" it means B already knows and it sounds like A has already told B about the appointment and reconfirm it.

I'm not a Korean expert, but I've lived in Korea for several years now. I have noticed that the younger generation (like my students), are using "알아." in the present tense to mean "I know." It could be that times are changing. I'm pretty sure I've heard "알아" used in dramas, and Koreans ask me all the time "다 알아?" when they find out I can speak a little Korean and are curious about whether I might have understood their conversation or not.

Generally, the present tense of a verb is composed like this: word stem + ㄴ/는 + ending The word stem of 알다 is 알. As a rule, the present tense of 알다 must be 알는다. But, because 알다 is a ㄹirregular verb, ㄹ is omitted in front of 는. Thus, the present tense of 알다 is 안다. Here is some variation forms of 안다. 알아. 알아요. 압니다. 알고 있어. 알고 있어요. 알고 있습니다. For reference, here is a list of ㄹirregular verb. 알다,살다,멀다,울다,불다,놀다,들다,떠들다

알다 is infinitive of "to know" literally. But 알았어 means "I know", "Okay", "I see" and so ond. If I would say the present tense of 알다, 알고 있어( I have realized it). would be more likely the answer. 다아는데 can have the meaning that "I know though"...or "anyway I know it so what?" "I knew it already" or " everyone knew it except you"