Difference between at last and finally

[Abecedarian]

Test No. express/elem-1 "Adding Up", question 9

He kept saying he didn't do it but in the end he said he had done it.

(a) at the end
(b) finally
(c) at last
(d) by the end

Test No. express/elem-1 "Adding Up", answer 9

He kept saying he didn't do it but finally he said he had done it.

Correct answer: (b) finally
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Why are "at last" and "by the end" wrong.

Thank you
Abecedarian

[Torsten]

At last and finally are rather similar in meaning as they suggest that we have been waiting for something for a long time. However, at last is normally used only for things that you are pleased have happened whereas finally can be used for both positive and negative things.
By the end means at some point before the end.
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Test Of English for International Communication
TOEIC Preparation & TOEIC Vocabulary

[Abecedarian]