How to solve this problem?

I wanted to make my own business on the Internet by making a Minecraft server and also making some stories and guides to sell but first I need to purchase a website and then make my PayPal. I'm 13 years old, my Mom won't make me do it, she doesn't trust Internet. You know elderlies don't know much about Internet. I wanted to but she doesn't agree. I did my best at school and got high grades and I told her to give me paypal and then she still doesn't give an exchange for my hard work. Can anyone help me or give advices that can make me understand my mother.

Are you taking a technology course at school? If you are, you're probably a good pupil. I'd ask the teacher if they would talk to your mom about how skilled you are at your studies in that area.

But realize that desinging the product is about 1/4 of what you have to know to run a successful website business. Have you studied business and business finance at all? You need to do that first.

It's not that 'elderlies' don't know much about Internet, it's because younglings like yourself are not aware of the cost of these things.

All you need to make PayPal is a bank account. Just open an account with $100, then withdraw all but $10 and you are good to go. You just need to find somebody who can lend you $90 for a week, if you don't already have that amount.

Make a business plan, showing how much you need to spend on stuff and how much stuff you expect to sell. You need to justify the projected sales, maybe from somebody else's Minecraft server. If the business plan is solid and the investment modest, then your mum may reconsider.