School cafeteria lunch prices will rise modestly this year in districts that pad their food-service budgets with federal money designed to feed low-income children, under new federal rules posted Monday,

The new interim rules, designed to make school lunch prices better reflect their costs, will take effect July 1. They were submitted to the Federal Register on Monday.

They call for full-cost or “paid” lunches to increase by 5 or 10 cents per meal in the 2011-12 school year.