~고라도 and ~더라도 (and also ~서라도)
The three can be used interchangeably sometimes, but not always.
You can think of -더라도 as the base form, and -서라도 and -고라도 derived ones with additional connotations.
* X-더라도 = even if X. 이 일은 무슨 일이 있더라도 해야 한다.
* X-서라도 (-서 하더라도) = even if by doing X. (i.e. X is a crucial part for the main action)
* X-고라도 (-고 하더라도) = even if it means/involves X; even if one has do X first before doing the main thing.
To fully understand them, you need to know the base forms -서 and -고 which underlies the two.
* X-(아/어)서 Y-하다 = do X to do Y. "차를 팔아서 돈을 마련하자". (It also has another usage signifying the reason)
* X-고 Y-하다 = do X and then Y, where X and Y are clearly separable. "밥 먹고 나가거라".
Examples:
1 돈을 내더라도 배워야 된다고 생각하거든요(O)= I think I should learn (it) even if I have to pay for it (simplest).
2 돈을 내고라도 배워야 된다고 생각하거든요(O). (They are hard to distinguish in English)
3 돈을 내서라도 배워야 된다고 생각하거든요(?).
* #1 and #2 are natural and very close in meaning. #3 is less so because we idiomatically say 돈을 내고 배우다, not 돈을 내서 배우다.
1. 대출을 받더라도 집을 사야겠다 (?). 대출을 받다(take out a loan) is mentioned as something that might come up.
2. 대출을 받아서라도 집을 사야겠다 (O). 대출을 받다 is brought up as the essential means to buying the house - natural.
3. 대출을 받고라도 집을 사야겠다 (?). Not natural because we say 대출을 받아(서) much more than 대출을 받고.
* Taking out a loan is the required means to buying a house, so #2 sounds the most natural.
1. 그는 죽더라도 고국에 돌아가고자 했다(O) = He wanted to go back to his country even if he might die doing that.
2. 그는 죽어서라도 고국에 돌아가고자 했다(O) = He wanted to go back even as a dead body.
3. 그는 죽고라도 고국에 돌아가고자 했다(X) = Wrong because 죽고 고국에 돌아가다 is strange.
* 죽어서 돌아가다 is commonly said, while 죽고 돌아가다 is not, because 죽어서 is closer to 죽은 상태로 than 죽고.