Here are some ways you can convince your parents.
- try to give them a budget or ask for one that they are ok with and see if you can afford it.
- ask them if you can pay half and they match that. Ask them what you can do to earn more money to pay for the computer.
- Tell them that the gaming pc will last you a long time and in the future a new pc being needed will be very unlikely. In addition to this, you won’t need to buy a new pc because you can constantly upgrade your pc.
- building a new pc is very easy and there are many good tutorials online that will help you.
- your new pc will be very good for school work(good cpu and ram)
- Tell them that building a pc is a good way to learn about computers.
- wait for black friday and tell them that there are very good deals for new parts and the build will be cheap(its 1/1/19 at the time of my answer so this one isn’t very good)
Just show them that you have done some research and that the pros out-weight the cons. I assume you are trying to justify the reasons to build your own pc versus just buying a pc.
Off the bat, I’d say that building a pc yourself is more economical and you will get more performance per dollar spent, rather than purchasing a pre-built pc. Plus it can be an educational experience, as you get to learn the pieces of hardware that go into a PC.
Browse through online build guides so that you can confirm whether all the hardware is compatible and go from there. For example: