Each county maintaining a subsidized receiving home shall submit to the department of human services by the tenth of each month or the first of each quarter, that is, January, April, July, and October, respectively, an itemized statement of the cost of subsidizing each licensed receiving home, and an itemized statement of the boarding care and special needs provided each child placed in the home during the preceding month or quarter. Within thirty (30) days after receipt of the statement, the department shall reimburse the county in the amount of fifty percent (50%) of the statement, so long as the cost of the subsidy, boarding care and special needs of any one (1) child does not exceed the amount specified in the contract entered into by the county, the department and the receiving home.