-더라도

-더라도 means "even if (we suppose) this happens": the main clause stays true or must still be done regardless.

대조·양보Contrast & concession

Han: Being sick yesterday is a real past fact, not an assumption, so -더라도 sounds odd; use -았/었는데도 (or -지만) for things that actually happened.

Examples

비가 오더라도 경기는 예정대로 진행됩니다.Even if it rains, the match will go ahead as planned.

조금 비싸더라도 품질이 좋은 걸로 사고 싶어요.Even if it's a bit expensive, I want to buy a good-quality one.

아무리 바쁘더라도 아침은 꼭 드세요.However busy you are, be sure to eat breakfast.

시험에 떨어지더라도 너무 실망하지 마세요.Even if you fail the exam, don't be too disappointed.

V/A+더라도

N+이더라도

past: V/A+았/었더라도

바쁘다 → 바쁘더라도, 비가 오다 → 비가 오더라도, 학생 → 학생이더라도, 알다 → 알았더라도

It is mainly used for hypothetical or assumed situations. For something that actually already happened, -았/었는데도 or -지만 is usually more natural.
The main clause very often expresses advice, a command, a promise or determination (-(으)세요, -지 마세요, -(으)ㄹ 거예요, -아/어야 해요).
For a past assumption ("even if it had…"), put 았/었 before -더라도 (알았더라도); do not attach -겠- to it.
It is often strengthened with 아무리 (however much) or 비록 (although), especially in formal speech and writing.

Wrong: ~~어제는 몸이 아프더라도 회사에 갔어요.~~

Right: 어제는 몸이 아팠는데도 회사에 갔어요.

Being sick yesterday is a real past fact, not an assumption, so -더라도 sounds odd; use -았/었는데도 (or -지만) for things that actually happened.

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