Every employee of the state whose service is covered by an agreement entered into under §§8-38-103 and8-38-104 shall be required to pay for the period of such coverage, contributions, with respect to wages, as defined in §8-38-101, equal to the amount of the employee's tax which would be imposed by the “Rate of Tax” sections of the Federal Insurance Contributions Act (26 U.S.C. §§ 3101 et seq.), if such services constituted employment within the meaning of that act. Such liability shall arise in consideration of the employee's retention in the service of the state, or the employee's entry upon such service, after the enactment of this chapter.