The holder of an exploration permit may, prior to expiration of the annual period for which such permit was issued, or prior to expiration of the annual period for which such permit was renewed, file with the department an application for renewal of such permit for the ensuing annual period. No such application for renewal shall be filed, nor shall the permit be renewed, for more than four successive annual periods following expiration of the annual period for which such permit was issued. No rental shall be payable for the first annual period for which a permit may be renewed. The rental for each of the three subsequent annual periods following the first annual period for which a permit may be renewed shall be one dollar for each acre of state land for which the application for renewal is filed. Upon receipt by the department of the application for renewal, and the affidavit of expenditure of the required amount in exploration during the current annual period or a sum equal thereto, together with such other proof in support of such expenditure as the commissioner by regulation may prescribe, and payment to the department of the rental for the ensuing annual period, all prior to expiration of the current annual period, the commissioner shall issue a renewal of the permit for the ensuing annual period.