Paying For The Prefix

A support assistant sends a 14,000-token prefix on every turn: tool definitions, policy text, and the customer's account snapshot. A session runs 20 turns, arriving about 40 seconds apart, so a 5-minute cache never expires between them. The provider prices this model at $3 per million input tokens, charges 1.25x base for a 5-minute cache write, and 0.1x base for a cache read.

You place one cache breakpoint at the end of the 14,000-token prefix. Turn 1 writes the cache; turns 2 through 20 read it.

What does the prefix cost across the whole session, and what did it cost before caching?