It seems likely that by the end of the week, the costs involved in the construction of the bridge . . . . . . . . by the Ministry.

Solution (By Examveda Team)

Option A: would have been announced - This suggests a hypothetical situation in the past related to a future time. While grammatically possible in some contexts, it doesn't fit the direct statement implied in the question.
Option B: have been announced - This is present perfect tense, indicating an action completed in the past with relevance to the present. It doesn't fit the future timeframe "by the end of the week."
Option C: would be announced - This expresses a future intention or prediction, but it doesn't emphasize the completion of the action *before* the end of the week.
Option D: are being announced - This is present continuous passive, indicating an action in progress now. It's incorrect because it contradicts the future timeframe.
Option E: will have been announced - This is the future perfect passive tense. It correctly indicates that the action of announcing the costs will be completed by the end of the week.

Therefore, the correct answer is Option E: will have been announced. It accurately conveys the idea that the announcement will be finished before the end of the week.