This is the 4072nd most frequent Korean word.
있어도
"Even if (something/someone) exists" or "Even if (something/someone) has."
In this sentence, "있어도" is used within a conditional clause meaning "even if." It suggests the hypothetical presence of something but states that this doesn't affect the main statement.
그 책은 내 방에 있어도 나는 잘 모른다.
Even if that book is in my room, I am not familiar with it.
Here, "있어도" is used to contrast the availability of time (having time) with the personal feeling of busyness, emphasizing that one condition does not negate the other.
시간이 있어도 항상 바쁜 느낌이 듭니다.
Even though there is time available, I always feel busy.
In this example, "있어도" highlights the presence of a condition (having a lot of money) while stating an outcome (unable to buy happiness), indicating the independence of the latter from the former.