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If you have not purchased a package that includes automated backup, I cannot see, how you can expect to get it.
It's like not signing a service contract on your car and then complain that if it breaks down, you will have to pay to get it fixed.
Automated backups is a selling point that costs extra - just like additional space and traffic limits - if you want it, I'm sure your hosting company would love to sell you a bigger package with more services in it (just a guess, though, I don't know your hosting company)