I know I ....... the letter earlier today.

[Freeguy]

I know I ....... the letter earlier today.

1. have had to post
2. need to post
3. ought to post
4. must have posted
5. could have posted

I think No.5 would be natural. However, I don't know the grammatical reason behind of that.

 

[Raymott]

4. is also possible, but 5 is most likely.
5. "I know I could have posted the letter earlier today. But I didn't have a lot of time, so I posted it this afternoon."
5. "I know I could have posted the letter earlier today. I posted a lot of mail, and that letter could have been among the others"
4. "I know I must have posted the letter earlier today. I posted everything in the "out box". If the letter was there, I must have posted it."