The first problem with Acts 16:31 in the word "believe" is a mistranslation. "Believing only in the Lord Jesus will avail nothing. The mistranslated words believe, believer, and believing come from the Greek word Pisteuo. The word pisteuo used 148 times in the NT could not be correctly translated into the English language because the English language has no verb form of the the Greek word Pisteuo. The definition of the Greek word Pisteuo is "A personal surrender to Him,(our lives) and a life inspired by such surrender". Which means, what saves you and your household is when a called out one responds to the unmerited favor of Grace with Pisteuo (Faith), You would be continually surrendering your life to Him each day, all day if necessary, and live a live inspired by this surrender. Which is making all the little daily decisions with the understanding that your life is no longer yours anymore but His now. If this life of Pisteuo {faith} is genuine, you can expect (not desire) the Grace deposit to be put in you. This begins an entirely new discussion, but i hope and understand that in this state of being the Scripture reads correct, "you, and your household will be saved." I also understand there are very few in this state of being due to the misunderstanding of the word Pisteuo.