I read in an old grammar book that ni was actually a fairly late construct and that in Swedish history, there was another extremely archaic word ('I'?) which is directly related to U in Dutch and You in English. In fact, Wikipedia supports this "ni is derived from an older pronoun I, 'ye', for which verbs were always conjugated with the ending -en. I became ni when this conjugation was dropped; thus the n was moved from the end of the verb to the beginning of the pronoun."
