In counties having a population of 99,000 or less according to the 1990 federal decennial census, after the state assumes responsibility for salaries and benefits of juvenile probation officers and staff of juvenile probation services, financial support from those counties for these functions shall be phased out over a five-year period. In the initial year of each county's transition, the county shall pay to the Juvenile Probation Services Fund in the State Treasury a sum equal to the total amount expended by the county during fiscal year 1997-98 for salaries and fringe benefits of juvenile probation officers, excluding the amount reimbursed by the state through salary subsidy payments, and staff of juvenile probation services as well as expenditures for supplies, travel, and administrative costs which can be documented. Each county shall enter into a contract with the state which establishes the amount to be paid and the terms of payments over the years of transition. The amount shall specifically exclude the salaries of staff and expenses of juvenile detention facilities and shelter care facilities. For each of the years two through five after transition begins, the annual amount paid by each county to the state shall be reduced by an additional 20 percent of the initial year's amount so that at the end of the five-year period, the county shall not remit any reimbursement to the state. Remittance for the reimbursement from the county shall be made by the tenth of each month to the Juvenile Probation Services Fund in the State Treasury.