Upon receipt of such annual report, the Secretary of Mines and Mineral Industries shall make an investigation of the operation and shall charge the area of land actually affected by strip mining during the year for which said report is filed against the bond or deposit filed by the operator at the established rate per acre of the area of land affected, but in no case shall the bond or deposit retained by the Secretary of Mines and Mineral Industries be less than five thousand dollars ($5,000). Should the area of land actually affected exceed the estimate made by the operator at the time of the application for the permit, the operator shall file an additional bond at the established rate per acre of the area of land affected over and above his estimate: Provided, That an additional bond need not be filed where the number of acres of land actually affected multiplied by five hundred dollars ($500) does not exceed the sum of five thousand dollars ($5,000), except in those instances where the secretary has found it necessary to increase the rate per acre. If the work contemplated by the permit the bond be not completed, but the area of land actually affected by strip mining during the year is less than the estimate, the secretary shall issue a release of the excess of the bond or deposit upon which liability has not been charged, as aforesaid: Provided, That in no case shall any bond or deposit be released or reduced to an amount less than five thousand dollars ($5,000).