Eunhi's answer is great. But I would like to add a bit more details since I think 알아/요 and 알았어/요 could have a slight difference in the meaning. 알아요 is used as the meaning of "I know" (I actually know it. I already knew that in advance.) but 알았어요 is more likely to mean "Okay" (Okay, I will. I got to understand it just now) And if you omit '-요' from any of these, it becomes 반말(the language that we use to younger/same aged close people)

I would say "알았어 " is the way to use for someone younger than you or use them between the same age group and also it is not very polite form to be used for older person. depends on the tone of voice it could be rude too if responded abruptly. it is a short version of "알았어요" which is polite form of previous one. meaning both the same: " i know or i understood" Hope it helps

I agree with Miss Tangerine on "알았어(요)"^^/ Itu maksud "saya dapat" tapi "알아요" maksud "saya tahu" \^o^/