1) Get a new DNS server. I use http://dnspark.net/ and even though their website is very ugly and there's no API, they're tremendous value at $10 - $14 per year
2) In your registrar's page (godaddy) change your DNS servers for your domain to whatever your new ones are.
$0.50 per hosted zone / month for the first 25 hosted zones
$0.10 per hosted zone / month for additional hosted zones
$0.500 per million queries – first 1 Billion queries / month
$0.250 per million queries – over 1 Billion queries / month
I host about 70 zones and pay less than 20 dollars a month. There's no minimum, so I would expect a single zone to cost less than $2. You would need to get 10 million queries to reach $6.
[Edit: Facepalm - I just realized you said per year]
1) Get a new DNS server. I use http://dnspark.net/ and even though their website is very ugly and there's no API, they're tremendous value at $10 - $14 per year
2) In your registrar's page (godaddy) change your DNS servers for your domain to whatever your new ones are.