a. Any member of the retirement system who:
(1) heretofore entered or shall hereafter enter city-service as a member of the uniformed force of the department of sanitation, as such force is defined in subdivision a of section 13-154 of this chapter; and
(2) has heretofore completed or shall hereafter complete not less than twenty years of service as a member of such uniformed force; and
(3) has heretofore completed or shall hereafter complete not less than twenty-five years of allowable city-service, including the service mentioned in paragraph two of this subdivision a; and
(4) is serving in the department of sanitation as commissioner thereof or as the secretary to such department or as the confidential investigator thereof, at the time of the filing of an application for service retirement as hereinafter in this subdivision authorized; and
(5) at the time of such filing, is required to make contributions to the retirement system at a rate calculated on the basis of a service-fraction of not less than one one-hundredth of his or her final compensation; may retire upon written application to the board setting forth at what time, not less than thirty days subsequent to the execution and filing thereof, he or she desires to be retired, and upon retirement for service he or she shall receive, on account of the first twenty-five years of his or her city-service, in lieu of any smaller retirement allowance for such period of service otherwise provided for by this chapter, a minimum retirement allowance which shall be equal to one-half of his or her annual salary or compensation when so retired.
b. There shall be added by the city, whenever required, a further pension of such amount which, together with the member's annuity based on accumulated deductions from his or her pay during his or her first twenty-five years of city-service (including regular interest to the date of completion of such period of city service), shall be sufficient to provide him or her with a minimum retirement allowance, on account of the first twenty-five years of his or her allowable city-service, equal to one-half of his or her annual salary or compensation when so retired. For the purpose only of determining the amount of the additional pension contributions by the city that may be required, the member's annuity shall be computed, as it would be, (a) if it were not reduced by the actuarial equivalent of any outstanding loan, (b) if it were not increased by the actuarial equivalent of any additional contributions, (c) if it were not reduced by reason of the member's election to decrease his or her annuity contributions in order to apply the amount of such reduction in payment of his or her contributions for old-age and survivors insurance coverage, (d) as it would be without any optional modification.
c. For city-service by such a member of the retirement system in addition to and in excess of twenty-five years, there shall be added to the retirement allowance to which he or she is entitled under subdivisions a and b of this section:
(1) an annuity which shall be computed in the following manner:
(a) There shall be added together: (1) the total amount of the accumulated deductions of such member, whenever made, as the same are on the date of his or her retirement, including all voluntary, additional contributions, whenever made; and (2) the amount of any loan to such member outstanding as of the date of his or her retirement.
(b) There shall be added together: (1) the amount of the accumulated deductions of such member, as of the date on which he or she completed twenty-five years of allowable city-service, exclusive of the value, as of such date, of all of his or her voluntary, additional contributions made up to and including such date; and (2) the amount of any loan to such member outstanding on such date.
(c) The annuity to which such member shall be entitled under this paragraph one shall be the actuarial equivalent of the remainder obtained by subtracting the sum computed pursuant to subparagraph (b) of this paragraph from the sum computed pursuant to subparagraph (a) of this paragraph.
(2) a pension which shall be equal to one service-fraction of such member's final compensation multiplied by the number of his or her years of allowable city-service from the day after he or she completed twenty-five years of allowable city-service to the date of his or her retirement; and
(3) a pension which shall be the actuarial equivalent of the reserve-for-increased-take-home-pay to which he or she may be entitled, if any, for the period from the day after he or she completed twenty-five years of allowable city-service to the date of his or her retirement.