a. (1) Except as provided in paragraph three of this subdivision a, any contributor who has been a member of the retirement system and has had five or more years of accredited service, who discontinues service in the schools or colleges of the city other than by death or retirement and who does not withdraw his or her accumulated deductions shall have a vested right to receive a deferred retirement allowance on attaining the age at which he or she would first be eligible for retirement had he or she remained in service but in no case, except as otherwise provided in paragraph two of this subdivision, prior to the date he or she attains the age of sixty years. Such member shall be known as a discontinued member.
(2) A discontinued member who has such vested right when he or she attains the age of fifty-five years and who was an age-fifty-five-increased benefits pension plan contributor when he or she discontinued service shall be entitled to receive a deferred retirement allowance under this section on the date when he or she attains the age of fifty-five years.
(3) The provisions of this section shall be inapplicable to a twenty-year pension plan contributor.
b. The deferred retirement allowance provided by this section shall vest automatically upon such discontinuance of service by such member and shall become payable on the day he or she reaches the age at which he or she would first be eligible for retirement had he or she remained in service but in no case prior to the date he or she attains age sixty, except as otherwise provided in paragraph two of subdivision a of this section.
c. (1) In the case of any discontinued member who was not an age-fifty-five-increased-benefits pension plan contributor when he or she discontinued service, the deferred retirement allowance provided for in this section shall be determined in accordance with the provisions of section 13-554, except that where the total service for any discontinued member whose retirement allowance is required to be determined pursuant to this paragraph one is less than twenty-five years, the pension shall be based on one per cent of this average salary for each year of accredited service.
(2) In the case of any discontinued member who was an age-fifty-five-increased-benefits pension plan contributor when he or she discontinued service, the deferred retirement allowance provided for in this section, shall, subject to the provisions of subdivision i of this section, be determined in accordance with the provisions of such section 13-554 governing the retirement allowance of an age-fifty-five-increased-benefits pension plan contributor, in the same manner as if he or she had retired for service on the date on which he or she attained the age of fifty-five years. In any case where, for the purpose of computing such retirement allowance, his or her average salary is required to be determined pursuant to subdivision eighteen of section 13-501 of this chapter, any reference in such subdivision to salary earnable during a period preceding the date of retirement shall, for the purposes of this paragraph two, be deemed to mean salary earnable during an equal period preceding the date of his or her discontinuance of service and any reference in such subdivision to selection of a period of service prior to the date of retirement, shall, for the purposes of this paragraph, be deemed to mean selection of such period prior to the date on which such discontinued member attains the age of fifty-five years.
d. Interest on the accumulated deductions and on the reserve-for-increased-take-home-pay of a discontinued member shall be credited after the discontinuance of service at the same rate as prior to the discontinuance.
e. If a member who has withdrawn from the service should die before becoming eligible for a deferred retirement allowance under this section his or her accumulated deductions and his or her reserve-for-increased-take-home-pay shall be paid to his or her beneficiary, and in the absence of a designated beneficiary, to his or her estate.
f. A member, who has withdrawn from the service in accordance with the provisions of this section, may elect any of the options available under the provisions of section 13-558 providing he or she files with the retirement board an application for such option prior to the day he or she becomes eligible for a deferred retirement allowance.
g. A member who has resigned from service may withdraw his or her accumulated contributions at any time subject to the limitations contained in section 13-541 of this chapter. The withdrawal of a member's accumulated contributions shall terminate his or her right to a vested deferred retirement allowance.
h. Subject to the provisions of section 13-549 of this chapter (relating to deferred eligibility of certain retirees, withdrawn contributors and discontinued members for benefits under certain pension plans), a member who has discontinued service but has not withdrawn his or her accumulated contributions and is subsequently restored to service in the city's schools or colleges, shall be entitled to the service credit and status to which he or she was entitled immediately prior to his or her withdrawal and shall also be credited with interest on his or her accumulated deductions and on his or her reserve-for-increased-take-home-pay between the time of his or her withdrawal and the time of his or her restoration to service.
i. (1) In any case where:
(a) a contributor:
(i) on or after July first, nineteen hundred sixty-nine, re-entered member-service (as defined in subdivision fifteen-a of section 13-501 of this chapter) or shall hereafter re-enter member-service; or
(ii) on or after July first, nineteen hundred seventy, first enters member-service; and
(b) such contributor, while an age-fifty-five-increased-benefits pension plan contributor and before completing four years of member-service after such re-entry or first entry into member-service, as the case may be, discontinued service so as to become a discontinued member; and
(c) his or her right to receive a deferred retirement allowance as a discontinued member is not terminated; the deferred retirement allowance to which he or she is entitled as a discontinued member shall be computed as provided for by paragraph two of subdivision c of this section, except as otherwise provided in paragraph two of this subdivision h.
(2) The pension component of such deferred retirement allowance shall not be as prescribed by paragraph two of such subdivision c, but shall instead be the larger of:
(a) a pension determined pursuant to the method of computation set forth in paragraphs one to five, inclusive, of subdivision f of section 13-549 of this chapter (relating to computation of the pension of certain retirees having deferred eligibility for benefits under certain pension plans); or
(b) the pension to which he or she would have been entitled under the provisions of paragraph one of subdivision c of this section, if he or she had not been an age-fifty-five-increased-benefits pension plan contributor when he or she discontinued service.
(3) The provisions of this subdivision (i) shall apply to any contributor who re-entered or shall re-enter member-service under the circumstances set forth in paragraph one of this subdivision, whether or not such re-entry was or shall be with credit for service and status at the termination of his or her prior membership in the retirement system.
j. Notwithstanding any other provision of law, a discontinued member with ten or more years of credited service in such system who dies before a retirement benefit becomes payable and who is otherwise not entitled to a death benefit from the system shall be deemed to have died on the last day that he or she was in service upon which his or her membership was based for purposes of eligibility for the payment of a death benefit pursuant to the provisions of section 13-542 or 13-543 of this title. The death benefit payable in such case shall be one-half of that which would have been payable had such member died on the last day that service was rendered.