Dario Iacoponi, 15, a pupil at the London Oratory School which Tony Blair's two sons Euan, 14, and Nicky, 12, attend, kept a diary of his philosophical thoughts on life in the two months leading up to his death.
After weighing up the pros and cons, he decided to commit suicide and planned it meticulously. He taught himself to use his father's shotgun and worked out how to fire it with a wooden spoon. He then waited until neither of his parents was at home before carrying out the plan last month.
Dr John Burton, the West London coroner, said it was clearly a considered process and Dario "came down on the side of suicide".
The inquest heard that the teenager was a brilliant pupil who had already passed six GCSEs at A* or A grades a year early. He played the violin and piano and was hoping to study law at Yale or Harvard. But a darker side to his character emerged in his diaries which were discovered by police. They spoke of his difficulties in coping with life, although there was little, or no mention, of any specific problem such as bullying.
Dario, an only child, was found by a 20-year-old lodger at the family's home in Ealing, west London. He had a shotgun by his side.
His father, Pietro, a translator, was in Switzerland on business, and his mother, Saleni, a teacher, was at an amateur dramatics class.
Inspector Colin Nursey, who found five diaries covering the last year of Dario's life, said there was a reference in them contemplating suicide. "He would not leave a note, he was very specific about that," he said.
Neither parent was in court, but Nadia Taylor, a family friend for the past 15 years, told the inquest that Dario was "always a very sociable and very friendly person". She said: "We are all very shocked. It all came as a surprise to us that he felt this way."
But Dr Burton said he could see no other conclusion than that Dario had taken his own life. "He has made it clear that he did so. That is the only verdict that I can return.
"He was quite stoical about it. He did not fear death. He decided on balance that life is not good and points out that the mathematics he has used are indisputable and that is his last entry. It was a considered process."
Dario's headmaster, John McIntosh, has said he was baffled and the school was shocked.