Explanation:

- Option 1: will have reached

- This is the correct answer.

- It uses the future perfect tense, which indicates an action that will be completed before or by a specific time in the future.

- Fits perfectly with "By this time next week" to suggest completion by that time.

- Option 2: would have reached

- Implies a conditional scenario or a situation dependent on another condition.

- Not suitable here since there is no condition mentioned.

- Option 3: would reach

- Uses the conditional mood, implying future intentions or possibilities that depend on certain conditions.

- Doesn't fit the sentence as there are no conditions involved.

- Option 4: shall reach

- Indicates a future intention or promise.

- Doesn’t imply completion by next week, as needed for this sentence.