a. Subject to the provisions of subdivision b of this section, a contributor shall not be required to continue to contribute to the annuity savings fund after he or she shall have become eligible for service retirement. All contributions made thereafter to such fund shall be voluntary. However, this subdivision a shall not apply to a contributor who elects to contribute at a rate not in excess of fifteen per centum in accordance with the provisions of subdivision two of section 13-521 and paragraph d of subdivision one of section 13-554, as amended; nor shall this subdivision apply to a member who became a contributor to the teachers' retirement system subsequent to April thirtieth, nineteen hundred sixty-three.
b. The provisions of subdivision a of this section shall be inapplicable to a twenty-year pension plan contributor and to an age-fifty-five-increased-benefits pension plan contributor.
c. A twenty-year pension plan contributor shall not be required to contribute to the retirement system after the later of the following dates:
(1) the date on which he or she becomes eligible to retire for service; or
(2) the date on which his or her accumulated deductions equal his or her minimum accumulation.