Annual costs depend on a lot of things, as others have posted. If one of your goals is to keep the cost down...
- get a well-bred dog from a reputable breeder & pick a breed with few health issues. The dog will cost more to buy, but on average it will pay off in terms of long-term good health with fewer vet visits.
- get a small dog. Big dogs eat a lot! More food = more expense.
- get a dog that you can groom yourself = bath, nail trims, ear cleanings, teeth brushing.
- exercise the dog every day. Dogs maintained at the proper weight have a lot fewer health issues. And exercised dogs tend to chew less, which can save emergency trips to the vets for bowel obstructions, etc. And you won't have to spend money to replace things that have been chewed.
- keep your dog up-to-date on preventive meds & vaccinations, e.g. heartworm if a problem where you live.
Assuming you got a healthy dog to begin with, I think you could earn enough money doing odd jobs (babysitting, dog walking neighbors' dogs, mowing lawns) to pay for food and routine vet visits.
See the chart at the bottom of this web page.
The Cost of Dog Ownership - Affording a Dog
You can adjust the numbers up and down depending on your plans, add another column for the money you can make to help pay for it, and show it to your parents. If you can't come up with enough $$ to pay for all of it, maybe your parents would be open to paying for half of it if you show you can do your part by saving enough money to pay for the first year's upkeep. Good luck!