Colorful

Upon reaching the train station to death, a dejected soul is informed that he is "lucky" and will have another chance at life though he does not want it. He is placed in the body of a 14-year-old boy named Makoto Kobayashi, who has just committed suicide by an overdose of pills. Watched over by a neutral spirit named Purapura in the form of a little boy, the soul must figure out what his greatest sin and mistake in his former life was before his six-month time limit in Makoto's body runs out. He also has a number of other lesser duties he must complete, such as understanding what led Makoto to commit suicide in the first place and learning how to enjoy his second chance at life.
He finds Makoto did not like his family and he greatly dislikes them for the same reasons. He is contemptuous of his father who is an underdog at work, forced to work lots of unpaid overtime. Despite her efforts, he hates his mother who had an affair with a dance instructor, something his father seems to be oblivious of. His older brother Mitsuru has given up on him because he is too moody and has no friends at school or anywhere else. He discovers that a girl (Hiroka) he fancies sells sex to older men so she can have the clothes and things she wants. Shoko is a weird girl from Makoto's class who becomes suspicious of his unusual behavior so he tries to stay away from her. After he gets mugged and beaten up by some delinquents, Shoko comes to visit Makoto at his house, but he scares her off. In one of their subsequent encounters Purapura explains that Makoto will really die this time after his six months expire. However, when he befriends Saotome, a boy in his class who accepts outcasts such as him and treats them as equals, Makoto sees the joy in life for the first time. They spend some time together and they even begin studying for their high school entrance exam, something for which neither of them had any ambition before.
Knowing that his brother will never get accepted to a public high school due to his failing grades and lack of interest, Mitsuru announces that he will postpone his college entrance exams in order to allow his parents to save some money so they can send Makoto to a private school. Makoto refuses and tells his parents and brother that he has already chosen Tamegawa High (a public school he and Saotome agreed on earlier). An aggravated Mitsuru is unable to comprehend his unwillingness to accept his family's help and asks him if he enjoys tormenting his own family. Makoto breaks in tears and says that he just wanted to go to the same school his only friend is going to apply which leads to his parents accepting his wish. With his deadline reaching its end, Makoto meets with Purapura for one last time. He announces that he has found out what his former life's mistake was. He reveals that the soul was Makoto to begin with and that the mistake was his suicide. Purapura tells him that he will keep on living, but that he will also erase his memories of Purapura and the spirit world in order to make Makoto not think that he has any more chances. Before wiping his memories, Purapura advises him to live a colorful life.

Question: What kind of school are Makoto's parents saving for?
Answer: private