Why do people in spoken conversation sometimes say 간다 instead of 가요 when they are leaving? I thought 간다 was a written form.
In spoken conversation, "간다" has the meaning of leave or join the get-together. It is only used when communicating your action to other or others. Usually, it is a stronger tone than "가요" to make person or people aware of your action. So it is mainly used by a friend, or by a boss.
In written expression, "간다" has a much more general meaning.