The quick answer
Chemical cost varies with pool volume, sanitation system, weather, water balance, use and whether corrective treatment is needed.
There is no universal monthly number
A small covered pool and a large sunny pool have different demand. Season and swimmer load also matter.
Routine versus corrective chemicals
Routine sanitizer and pH control are different from algae cleanup, phosphate treatment or major stabilizer correction.
Stabilized products can add hidden cost
Convenient tablets add stabilizer. Excess CYA may eventually require water replacement, which adds cost.
Salt pools still use chemicals
Salt cells produce chlorine, but pH, alkalinity, stabilizer and salt still require monitoring and adjustment.
Reduce waste with testing
Reliable testing and measured dosing cost less than random additions. Good circulation and debris removal also reduce demand.