If you were to use azure table storage and use shared access tokens for authorizing access to query results, you could run the whole thing from any individual data center for under $500/month.
Assumption is that every IP (all 4.3 billion) had about 100 bytes of data stored about them. That is ~430gb of storage runs you $30/month. The 10 billion queries to that storage costs about $360/month. ($.0036 per 100,000 transactions)
Looks like the service is an IP lookup API. The sort of thing that many sites will hit once for each visitor. Most SaaS sites will never get anywhere near this, but things that do per-user or per-pageview queries (e.g. usage analytics) can get to billions of events per month with, say, 10k customers doing 1M hits each.
That's roughly 4k qps. Assuming it's a lightweight API a single server isn't out of the question. Nginx will handle 20k qps until the end of time on a tiny box serving static content.
Some live stats http://ip-api.com/docs/statistics