(C) Will allow.
Explain:
"The new computer system" is the main subject of this sentence.
"...designed for the post office" is the short form of a relative clause that modifies the main subject.
The new computer system will allow accounts to be managed over the internet.
Grammatically speaking, it's perfectly ok to omit the phrase "...designed for the post office". It just provides additional information for the main subject.
"...accounts" is an object, so we know that before it must be a transitive verb. (A), (B), (C), and (D) all satisfy this requirement. Because the main subject is singular, Both (A) and (B) are crossed out. (D) is not correct either as the sentence does not refer to any specific time as an interruption in the future.
Hope it helps!
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