In making and presenting the application for such payments to the United States, the county treasurer shall make application for payments based upon the estimated cost of the public services available for the benefit of the property in any such project and the tenants thereon, after taking into consideration the benefits which may be derived by the county or political subdivision from the project within its jurisdiction, but the amount shall not be in excess of the taxes which would result to the county and political subdivisions for said period if the real property of the project within the county were taxable. If, after the application is presented, the United States provides for the payment to be made in installments, it shall be the duty of the county treasurer to present a claim or bill to the United States for each installment as it falls due.