Which term: Answer, reply or respond?

Answer or reply are the most commmon verbs used for speaking or writing as a reaction to a question, letter etc.

Note that you answer a person, question or letter not answer to them but you reply to somebody or something:
I´m writing to answer your question.
I´m writing to reply to your question.

Although answer can be used with an object, it often sounds more natural without one:
I knocked on the door but nobody answered.


Reply is often used with actual words spoken:
`I won´t let you down`, he replied 

Respond is less common and more formal:
The directors were unwilling to respond to questions.

You can only answer a door or a phone.