considered, considering...

Is this sentence below correct?

Considered her offer carefully, you'll understand how generous she is with her money.

I think the sentence should be;
1) Having considered her offer carefully, you'll understand...
or
2) Considering her offer carefully, you'll understand...

I think "Having" before considered can't be omitted in 1).

If the original sentence is ok,
could you explain why the sentence is ok and how about 1) or 2)?

Thank you in advance.