まで and までに

When used in front of a temporal word, まで and までに can have different meanings. Let's take a look at the below examples:

３時まで手紙を書きました。
I wrote the letter until 3 o'clock.

３時までに手紙を書きました。
I finished writing the letter by 3 o'clock.

In the first sentence, the action (of writing a letter) is not completed until 3 o'clock. Whereas in the second sentence, the action is completed before 3 o'clock.