The formula
There's a one-off cost to read all your documents in (cheap, because searching is cheap). Then each month you pay to search and - the big one - to write answers. Each answer costs the snippets and instructions you feed in plus the words the AI writes back, times how many questions you get.
Questions
How much does a RAG app cost?
A small one-off cost to read your documents in, then a per-question cost that's mostly the AI writing answers. Searching and storage stay cheap next to that.
What costs more - searching or writing answers?
Writing answers, by a long way. Searching costs about a hundred times less, so put your effort into the answer-writing model and how much text you feed it.
How much does the storage (vector database) cost?
For small-to-medium apps, usually $0–$70 a month. Running it yourself costs only the server and storage underneath.