a. Notwithstanding any other provision of this title to the contrary, any contributor:
(1) Who:
(a) heretofore and 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, after having been, immediately prior to any such re-entry, a person whose last preceding member-service was terminated by retirement, withdrawal from membership in the retirement system or discontinuance of service so as to become a discontinued member, and at the time of his or her retirement, withdrawal or discontinuance of service so as to become a discontinued member, as the case may be, was not a twenty-year pension plan contributor or an age-fifty-five-increased-benefits pension plan contributor; or
(b) first enters member-service on or after July first, nineteen hundred seventy after having rendered city-service prior to the date of such first entry; and
(2) who:
(a) where eligible to elect to become a twenty-year pension plan contributor under section 13-547 of this chapter (relating to the twenty-year pension plan), elects to become such a contributor; or
(b) where eligible to elect to become an age-fifty-five-increased benefits pension plan contributor under section 13-548 of this chapter (relating to the age-fifty-five-increased-benefits pension plan), elects to become such a contributor; or
(c) becomes an age-fifty-five-increased-benefits pension plan contributor under the provisions of subdivision d of such section 13-548 of this chapter (relating to required membership in the age-fifty-five-increased-benefits pension plan) or subdivision d of section 13-547 of this chapter (relating to cancellation of election to be a twenty-year pension plan contributor); shall, until such contributor has rendered four years of credited service after such re-entry into member-service or first entry into member-service, as the case may be:
(i) be ineligible, if such contributor is a twenty-year pension plan contributor, to retire for service in accordance with the eligibility requirements for retirement under section 13-547 of this chapter (relating to the twenty-year pension plan); and
(ii) be ineligible to become entitled to the retirement allowance prescribed for retired twenty-year pension plan contributors by subdivisions f and g of section 13-547 of this chapter or to the retirement allowance prescribed for age-fifty-five-increased-benefits pension plan contributors by paragraph e of subdivision one of section 13-554 of this chapter, as the case may be.
b. (1) In the case of any contributor mentioned in subdivision a of this section who discontinued service as a discontinued member, the provisions of such subdivision shall be applicable to such contributor, whether or not he or she heretofore was or hereafter is receiving a deferred retirement allowance under section 13-556 of this chapter (relating to vested retirement rights) at the time of his or her reentry into member-service and whether or not he or she heretofore was or hereafter is entitled, at the time of such re-entry, to credit for service and status prior to withdrawal as provided for in subdivision h of such section.
(2) In the case of any contributor mentioned in subdivision a of this section who re-entered member-service as a withdrawn contributor, the provisions of such subdivision shall be applicable to such contributor, whether or not he or she heretofore was or hereafter is entitled, at the time of such re-entry, to service credit and status prior to withdrawal as provided for in section 13-506 of this chapter (relating to withdrawn contributors who re-enter service).
c. Any twenty-year pension plan contributor or age-fifty-five-increased-benefits pension plan contributor to whom the provisions of subdivisions a and b are applicable, may, before he or she has completed a period of four years of credited service after his or her first entry into member-service or re-entry into member-service, as the case may be, retire from service upon written application to the retirement board setting forth at what time subsequent to the execution of such application he or she desires to be retired. Such application shall retire such contributor at the time so specified, provided he or she has reached or passed the age of fifty-five years.
d. Any twenty-year pension plan contributor or age-fifty-five-increased benefits pension plan contributor who retires pursuant to subdivision c of this section shall receive, in lieu of any other retirement allowance, a retirement allowance which shall consist of:
(1) an annuity which is the actuarial equivalent of his or her accumulated deductions at the time of such retirement; and
(2) a pension-providing-for-increased-take-home-pay which is the actuarial equivalent of the reserve-for-increased-take-home-pay to which he or she may be entitled, if any; and
(3) a pension as provided for by the applicable provisions of subdivision e, f or g of this section.
e. Any such contributor mentioned in subdivision d of this section, if he or she has not reached the age of sixty-five years at the time of such retirement and at such time is credited with at least twenty-five years of total-service, shall receive a pension which shall be equal to the sum obtained by adding together:
(1) the amount obtained by multiplying the number of years of city-service credited to him or her at such time by one per centum of his or her average salary; and
(2) the amount obtained by multiplying the number of years of prior outside service for which he or she is credited at such time:
(a) by one and two-tenths per centum of his or her average salary, if such contributor purchased credit for such service pursuant to subparagraph (j) of paragraph three of subdivision a of section 13-505 of this chapter (relating to purchase of credit for prior outside service by certain contributors who last entered member-service prior to July first, nineteen hundred seventy) or paid a purchase price therefor computed pursuant to item two of subparagraph (1) of such paragraph three; or
(b) by one and fifty-three one hundredths per centum of his or her average salary, if such contributor purchased credit for such service pursuant to subparagraph k of such paragraph three or paid a purchase price therefor computed pursuant to item three of subparagraph (1) of such paragraph three.
f. Any such contributor mentioned in subdivision d of this section, if he or she has not reached the age of sixty-five years at the time of such retirement and at such time is credited with less than twenty-five years of total-service, shall receive a pension which shall be equal to the sum obtained:
(1) by adding together:
(a) the number of his or her years of member-service rendered after his or her last entry into member-service; and
(b) the number of years of city-service, if any, which:
(i) were rendered by him or her prior to such last entry; and
(ii) do not exceed the number of his or her years of member-service rendered after such last entry; and
(iii) are credited to him or her at the time of such retirement; and
(2) by multiplying that part, if any, of the total period of service computed pursuant to paragraph one of this subdivision f, which part was rendered prior to July first, nineteen hundred seventy, by one and two-tenths per centum of his or her average salary; and
(3) by multiplying that part, if any, of the total period of service computed pursuant to such paragraph one, which part was rendered after June thirtieth, nineteen hundred seventy, by one and fifty-three one-hundredths per centum of his or her average salary; and
(4) by multiplying the number of years of prior outside service, if any, for which he or she is credited at the time of such retirement:
(a) by one and two-tenths per centum of his or her average salary, if such contributor purchased credit for such service pursuant to subparagraph (j) of paragraph three of subdivision a of section 13-505 of this chapter (relating to purchase of credit for prior outside service by certain contributors who last entered member-service prior to July first, nineteen hundred seventy); or
(b) by one and fifty-three one hundredths per centum of his or her average salary, if such contributor purchased credit for such service pursuant to subparagraph k of such paragraph three or paid a purchase price therefor computed pursuant to item three of subparagraph (1) of such paragraph three; and
(5) by adding together the products obtained pursuant to paragraphs two, three and four of this subdivision.
g. (1) Subject to the provisions of paragraph two of this subdivision, any such contributor mentioned in subdivision d of this section, if he or she has reached the age of sixty-five years at the time of such retirement, shall receive a pension which shall be equal to the sum obtained by computing with respect to such contributor the products specified in paragraphs one and two of subdivision e of this section, and by adding such products together.
(2) If a pension, as computed for such contributor pursuant to the provisions of paragraphs one to five, inclusive, of subdivision f of this section, is greater than such pension computed pursuant to paragraph one of this subdivision g, such contributor shall receive such greater pension.
h. (1) The normal rate of contribution of any twenty-year pension plan contributor or age-fifty-five-increased-benefits pension plan contributor to whom the provisions of subdivisions a and b of this section are applicable shall be as prescribed by the applicable provisions of section 13-547 of this chapter (relating to the twenty-year pension plan) governing the normal rate of contribution of a twenty-year pension plan contributor or the applicable provisions of section 13-548 of this chapter (relating to the age-fifty-five-increased-benefits pension plan) governing the normal rate of contribution of an age-fifty-five-increased-benefits pension plan contributor.
(2) Any twenty-year pension plan contributor or age fifty-five-increased-benefits pension plan contributor to whom the provisions of subdivisions a and b of this section are applicable shall, unless he or she retires for service within the applicable period of four years of credited service mentioned in such subdivision a, be entitled to the same rights, benefits and privileges as such a contributor, including rights, benefits and privileges in the event of death, retirement for superannuation pursuant to subdivision three of section 13-545 of this chapter or retirement for disability pursuant to section 13-550 or 13-551 of this chapter, as if such subdivisions a and b were not applicable to him or her.
(3) For the purposes of paragraph two of this subdivision h, the presumed retirement, under paragraphs a and b of subdivision two of section 13-545 of this chapter (relating to cases of presumed retirement in the event of death of a contributor) of a contributor who dies under such circumstances that he or she is deemed under such subdivision to have been retired, shall not be deemed a retirement for service mentioned in such paragraph two.