Certificates of registration shall expire on the last day of the month of December following their issuance and shall become invalid after that date unless renewed. It shall be the duty of the secretary of the department to notify every person registered under this chapter of the date of the expiration of the certificate of registration and the amount of the fee required for its renewal. Such notice shall be mailed to the registrant at his last-known address at least one month in advance of the expiration of such certificate. Renewal may be effected at any time prior to or during the month of December by the payment of a fee established by the department not to exceed the fees established for registration. Renewal of an expired certificate may be effected under rules promulgated by the department regarding requirements for reexamination and penalty fees.