A member may purchase service credit as provided in this section for periods of employment described in subsection (c) of this section for which the member is not otherwise entitled to service credit. A member who purchases service credit under this section shall: complete a claim for the service credit and file it with the Board of Trustees on the form that the Board of Trustees provides; and pay to the Board of Trustees an amount equal to the annuity reserve and pension reserve required to fund the additional allowance. The member shall pay for service credit purchased under this section in a single payment at retirement. A member may purchase service credit for a period of employment: not exceeding 10 years for out-of-state public school teaching service; not exceeding 10 years for public or nonpublic school teaching service; not exceeding 5 years for postsecondary school teaching service; not exceeding 10 years for federal service or out-of-state service with a political subdivision; or as an employee of a political subdivision of this State if the employee is not receiving retirement benefits from a political subdivision of the State for the same period of employment.