Many evangelicals speak of an "age of accountability"? Is this some subjective point; varying from person to person? For some is it 11, for some at puberty, while for others 13 or 14? What is the age of accountability? I see no Scriptural precedent or 'inference', if you prefer, for such a thing?
You are correct that there is no mention of an “age of accountability” in the Scripture. There is, however, a necessary inference that requires such a concept. The term is used to designate the point at which one becomes accountable before God. In other words, it is the point at which one becomes accountable for his sins. Calvinists and Roman Catholics believe that it is at birth because all who are born are stained with the sin of Adam. Scripture does not teach that concept. To the contrary, it teaches that little children are innocent for “of such is the Kingdom of heaven.” Mark 10:14. Little children cannot be saved because they are not lost. They are “safe” because they cannot sin. Understanding the gospel is required for the lost to be saved. Philips first question to the Ethiopian nobleman was “Understandest thou what thou readest?” Acts 8:30. A little child is incapable of understanding. When one reaches the age where he is capable of understanding he becomes accountable or reaches the “age of accountability.” It is different for different people. Some mentally incapacitated individuals who, though in their twenties or thirties or even older, never become more than “little children” in mind. Thus, they are never capable of understanding and never reach the “age of accountability.” Some who are raised in Christian home and are taught in bible classes before they can walk or talk are capable of understanding much earlier than others. Of course, this raises the question of what they must be capable of understanding. Notice that what is involved in the capacity to understand, not whether they in fact understand. Obviously, they do not need to capable of understanding everything. At a minimum they must be capable of understanding what sin is, what sin did to Christ and to man, and what Christ did to sin on behalf of man. Capacity to understand these events (not just the facts that can be recited) means that one is capable of understanding that he is lost and in need of a Savior and that Christ is that Savior. Appreciation for that understanding should lead one to cry out as on the day of Pentecost, “Men and brethren, what must we do to be saved?” The answer is still the same: “Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.” Acts 2:38.
You Must Hear the Gospel
You must hear the gospel and then understand and recognize that you are lost without Jesus Christ no matter who you are and no matter what your background is. The Bible tells us that “all have sinned, and come short of the glory of God.” (Romans 3:23) Before you can be saved, you must understand that you are lost and that the only way to be saved is by obedience to the gospel of Jesus Christ. (2 Thessalonians 1:8) Jesus said, “I am the way, the truth, and the life: no man cometh unto the Father, but by me.” (John 14:6) “Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.” (Acts 4:12) "So then faith cometh by hearing, and hearing by the word of God." (Romans 10:17)
You Must Believe
You must believe and have faith in God because “without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him.” (Hebrews 11:6) But neither belief alone nor faith alone is sufficient to save. (James 2:19; James 2:24; Matthew 7:21)
You Must Repent
You must repent of your sins. (Acts 3:19) But repentance alone is not enough. The so-called “Sinner’s Prayer” that you hear so much about today from denominational preachers does not appear anywhere in the Bible. Indeed, nowhere in the Bible was anyone ever told to pray the “Sinner’s Prayer” to be saved. By contrast, there are numerous examples showing that prayer alone does not save. Saul, for example, prayed following his meeting with Jesus on the road to Damascus (Acts 9:11), but Saul was still in his sins when Ananias met him three days later (Acts 22:16). Cornelius prayed to God always, and yet there was something else he needed to do to be saved (Acts 10:2, 6, 33, 48). If prayer alone did not save Saul or Cornelius, prayer alone will not save you. You must obey the gospel. (2 Thess. 1:8)
You Must Confess
You must confess that Jesus Christ is the Son of God. (Romans 10:9-10) Note that you do NOT need to make Jesus “Lord of your life.” Why? Because Jesus is already Lord of your life whether or not you have obeyed his gospel. Indeed, we obey him, not to make him Lord, but because he already is Lord. (Acts 2:36) Also, no one in the Bible was ever told to just “accept Jesus as your personal savior.” We must confess that Jesus is the Son of God, but, as with faith and repentance, confession alone does not save. (Matthew 7:21)
You Must Be Baptized
Having believed, repented, and confessed that Jesus is the Son of God, you must be baptized for the remission of your sins. (Acts 2:38) It is at this point (and not before) that your sins are forgiven. (Acts 22:16) It is impossible to proclaim the gospel of Jesus Christ without teaching the absolute necessity of baptism for salvation. (Acts 8:35-36; Romans 6:3-4; 1 Peter 3:21) Anyone who responds to the question in Acts 2:37 with an answer that contradicts Acts 2:38 is NOT proclaiming the gospel of Jesus Christ!
You Must Be Faithful Unto Death
Once you are saved, God adds you to his church and writes your name in the Book of Life. (Acts 2:47; Philippians 4:3) To continue in God’s grace, you must continue to serve God faithfully until death. Unless they remain faithful, those who are in God’s grace will fall from grace, and those whose names are in the Book of Life will have their names blotted out of that book. (Revelation 2:10; Revelation 3:5; Galatians 5:4)