§ 13-127 Contributions of the city and their use; contingent reserve fund.

   a.   The contingent reserve fund shall be the fund in which shall be accumulated the reserve necessary to pay all pensions and the reserve-for-increased-take-home-pay, and all death benefits allowable by the city on account of the city-service of members to whom prior-service is not allowable as provided in this chapter.

   b.   (1)   (a)   Subject to the provisions of subparagraph (d) of this paragraph and paragraph five of this subdivision, the city shall contribute to the contingent reserve fund:

            (i)   annually an amount to be known as the normal contribution; and

            (i-a)   all unfunded accrued liability installments as required by section 13-638.2 of this title or any other provision of law; and

            (i-b)   any other payments to the contingent reserve fund as required by applicable law; and

            (ii)   in each city fiscal year during the period beginning with fiscal year nineteen hundred seventy-seven-nineteen hundred seventy-eight and ending on the last day of fiscal year nineteen hundred seventy-nine-nineteen hundred eighty, one annual installment of an additional amount which shall be known as the original unfunded accrued liability contribution, and which shall be determined as provided for in subparagraph (a) of paragraph three of this subdivision; and

            (iii)   in each city fiscal year during the period beginning with fiscal year nineteen hundred eighty-nineteen hundred eighty-one and ending on the last day of fiscal year two thousand fourteen-two thousand fifteen, the annual installment, applicable to such fiscal year, of an additional amount which shall be known as the revised unfunded accrued liability contribution and which shall be determined as provided for in subparagraph (b) of paragraph three of this subdivision; and

            (iv)   in each city fiscal year during the period beginning with fiscal year nineteen hundred eighty-one-nineteen hundred eighty-two and ending on the last day of fiscal year two thousand twenty-two thousand twenty-one, the annual installment, applicable to such fiscal year, of an additional amount which shall be known as the balance sheet liability contribution and which shall be determined as provided for in paragraph four of this subdivision; and

            (v)   in fiscal year nineteen hundred eighty-nineteen hundred eighty-one, the amount of one year's interest, at the rate of seven and one-half per centum per annum, on the amount of the balance sheet liability as of June thirtieth, nineteen hundred eighty, as determined pursuant to the provisions of paragraph four of this subdivision; and

            (vi)   in each city fiscal year, beginning with fiscal year nineteen hundred eighty – nineteen hundred eighty-one and ending on the last day of fiscal year nineteen hundred ninety-four – nineteen hundred ninety-five, the amount required to fulfill the city's obligation, if any, which accrued in such fiscal year, to make contributions on account of increased-take-home-pay; and

            (vii)   in each city fiscal year, beginning with fiscal year nineteen hundred eighty – nineteen hundred eighty-one and ending on the last day of fiscal year nineteen hundred ninety-four – nineteen hundred ninety-five, the amount required to fulfill the city's obligation, which accrued in such fiscal year under the provisions of subdivision twenty of section two hundred forty-three of the military law, to pay in behalf of members qualifying for such benefit, member contributions with respect to certain periods of the military service of such members.

         (b)   (i)   Subject to the provisions of item (iv) of this subparagraph, if the nineteen hundred eighty unfunded accrued liability adjustment determined pursuant to subparagraph (c) of paragraph three of this subdivision b is a credit, the total of the amounts required to be contributed to the contingent reserve fund in each city fiscal year, commencing with the nineteen hundred eighty-nineteen hundred eighty-one fiscal year and ending with the two thousand nine-two thousand ten fiscal year, pursuant to items (i), (iii), (iv), (v), (vi) and (vii) of subparagraph (a) of this paragraph and otherwise pursuant to law shall be reduced by the amount of one annual installment of such nineteen hundred eighty unfunded accrued liability adjustment.

            (ii)   Subject to the provisions of subparagraph (d) of this paragraph, if the nineteen hundred eighty unfunded accrued liability adjustment determined pursuant to subparagraph (c) of paragraph three of this subdivision is a charge, the city shall contribute in each city fiscal year, commencing with the nineteen hundred eighty-nineteen hundred eighty-one fiscal year and ending with the two thousand nine-two thousand ten fiscal year, in addition to the amounts required to be contributed under the provisions of subparagraph (a) of this paragraph, one annual installment of such nineteen hundred eighty unfunded accrued liability adjustment.

            (iii)   Subject to the provisions of item (iv) of this subparagraph, the total of the amounts required to be contributed to the contingent reserve fund in each city fiscal year commencing with the nineteen hundred eighty-two-nineteen hundred eighty-three fiscal year and ending with the two thousand eleven-two thousand twelve fiscal year pursuant to items (i), (iii), (iv), (vi) and (vii) of subparagraph (a) of this paragraph and the applicable provisions of items (i) and (ii) of this subparagraph and otherwise pursuant to law shall be reduced by the amount of one annual installment of the nineteen hundred eighty-two unfunded accrued liability adjustment determined pursuant to item (vi) of subparagraph (c) of paragraph three of this subdivision.

            (iii-a)   If the nineteen hundred eighty-five unfunded accrued liability adjustment determined with respect to any obligor pursuant to the applicable provisions of sub-items (A) to (G), inclusive, of item (vii) of subparagraph (c) of paragraph three of this subdivision b is a charge, the total of the amounts required to be contributed by such obligor to the contingent reserve fund in each city fiscal year commencing with the nineteen hundred eighty-five-nineteen hundred eighty-six fiscal year and ending with the two thousand fourteen-two thousand fifteen fiscal year pursuant to items (i), (iii), (iv), (vi) and (vii) of subparagraph (a) of this paragraph one and the applicable provisions of items (i) and (ii) of this subparagraph (b) and otherwise pursuant to law shall be increased by the amount of one annual installment of such nineteen hundred eighty-five unfunded accrued liability adjustment determined with respect to such obligor.

            (iii-b)   If the nineteen hundred eighty-five unfunded accrued liability adjustment determined with respect to any obligor pursuant to the applicable provisions of such sub-items (A) to (G), inclusive, is a credit, the total of the amounts required to be contributed by such obligor to the contingent reserve fund in each city fiscal year commencing with the nineteen hundred eighty-five-nineteen hundred eighty-six fiscal year and ending with the two thousand fourteen-two thousand fifteen fiscal year pursuant to items (i), (iii), (iv), (vi) and (vii) of subparagraph (a) of this paragraph one and the applicable provisions of items (i) and (ii) of this subparagraph (b) and otherwise pursuant to law shall be reduced by the amount of one annual installment of such nineteen hundred eighty-five unfunded accrued liability adjustment with respect to such obligor.

            (iv)   The installments of the nineteen hundred eighty-two unfunded accrued liability adjustment, and, if the nineteen hundred eighty unfunded accrued liability adjustment is a credit, the installments of such nineteen hundred eighty adjustment credit, shall be allocated among the city and other obligors required to pay public employer contributions on account of members, such allocation to be made in accordance with the shares of such installments attributable to them pursuant to the provisions of law prescribing their obligations to make or assume responsibility for employer contributions.

            (v)   For the purpose of effectuating the nineteen hundred eighty-eight unfunded accrued liability adjustment provided for in section 13-638.1 of the code, contributions to the contingent reserve fund on account of charges shall be made by responsible obligors (as defined in paragraph six of subdivision a of such section) or credits shall be allowed to such obligors against contributions otherwise payable by them, as the case may be, to the extent and in the manner provided for in such section. The annual determination of the normal contribution for fiscal years occurring during the period beginning on July first, nineteen hundred eighty-eight and ending on June thirtieth, nineteen hundred ninety-eight shall appropriately take account of the nineteen hundred eighty-eight unfunded accrued liability adjustment as provided for in such section 13-638.1 and the provisions of subparagraph (b) of paragraph two of this subdivision b shall be deemed to be conformably modified for such purpose.

         (c)   (i)   Any amount required by the provisions of items (iii), (iv), (v), (vi) and (vii) of subparagraph (a) of this paragraph and subparagraph (b) of this paragraph and section 13-704 of this title to be contributed to the contingent reserve fund in the city's nineteen hundred eighty-nineteen hundred eighty-one fiscal year or any subsequent fiscal year shall be payable with interest on such amount at a rate per centum per annum equal to the rate per centum per annum required to be used for the purpose of any actuarial valuation, determination or appraisal made to determine the amount of the normal contribution payable to the contingent reserve fund in such fiscal year.

            (ii)   Any amount required to be contributed to the contingent reserve fund in any fiscal year of the city preceding the nineteen hundred eighty-nineteen hundred eighty-one fiscal year shall be deemed to have been required to be paid with interest on such amount at a rate per centum per annum equal to the rate per centum per annum required to be used for the purpose of any actuarial valuation, determination or appraisal made to determine the amount of the normal contribution payable to the contingent reserve fund in such fiscal year.

            (iii)   It is hereby declared that the provisions of items (i) and (ii) of this subparagraph, insofar as they relate to provisions of this chapter or other laws requiring payment of employer contributions to the retirement system prior to the date of enactment of the act which added this subparagraph, express the intent of such provisions of this title or other laws requiring such payment.

            (iv)   The city and all other responsible obligors (as defined in paragraph ten of subdivision a of section 13-638.2 of this title) shall make all payments to the retirement system required by applicable law in accordance with the time of payment requirements set forth in subdivision c of section 13-133 of this chapter. Any responsible obligor which does not make all or any portion of such required payments to the retirement system in a timely manner in fiscal year two thousand twelve – two thousand thirteen, or in any fiscal year thereafter, shall be required to pay interest to the retirement system on such overdue amounts, as determined by the actuary. The actuary shall determine, at such time as he or she deems appropriate, interest payments on such overdue amounts using a rate of interest equivalent to the valuation rate of interest (as defined in paragraph eleven of subdivision a of section 13-638.2 of this title). Responsible obligors shall make such interest payments on overdue amounts to the retirement system in the manner and at such time as the actuary deems appropriate.

         (d)   The requirements of subparagraph (a) of this paragraph with respect to contributions to the contingent reserve fund and the requirements, if any, of subparagraph (b) of this paragraph with respect to contributions to such fund, and the requirements of subparagraph (c) of this paragraph with respect to payment of interest on contributions to such fund shall be subject to the provisions of sections 13-130, 13-131 and 13-132 of this chapter.

      (2)   Normal contribution.

         (a)   (i)   Notwithstanding the succeeding provisions of this subparagraph or the provisions of subparagraph (a-one), (b) or (c) of this paragraph, for fiscal year two thousand eleven – two thousand twelve, and for each fiscal year thereafter, the amount of the normal contribution payable to the contingent reserve fund shall be determined pursuant to the provisions of subparagraph (d) of this paragraph. Upon the basis of the latest mortality and other tables herein authorized and regular interest, the actuary shall determine as of June thirtieth, nineteen hundred eighty and as of each succeeding June thirtieth, the amount of the total liability for all benefits provided in this title, in articles eleven and fourteen of the retirement and social security law and in any other law prescribing benefits payable by the retirement system on account of all members and beneficiaries, excluding the liability on account of future increased-take-home-pay contributions, if any, and the liability for benefits attributable to the annuity savings fund, provided, however, that in determining such total liability as of June thirtieth, nineteen hundred ninety-five and as of each succeeding June thirtieth, the actuary shall include (A) the liability on account of future increased-take-home-pay contributions, if any, (B) the liability on account of future public employer obligations under the provisions of subdivision twenty of section two hundred forty-three of the military law, to pay in behalf of members qualifying for such benefit, member contributions with respect to certain periods of the military service of such members and (C) the liability for benefits attributable to the annuity savings fund.

            (ii)   For the purposes of subparagraphs (b) and (c) of this paragraph, the actuary shall determine, as of June thirtieth, two thousand and as of each succeeding June thirtieth, the total liability of the retirement system which shall be an amount equal to the sum of (A) the total liability for all benefits as determined pursuant to item (i) of this subparagraph, (B) the amount, as estimated by the actuary, of the total liability of the retirement system on account of all payments which the retirement system may be required to make for base fiscal years beginning on or after July first, nineteen hundred ninety-nine to the correction officers' variable supplements fund and the correction captains' and above variable supplements fund, and (C) the amount, if any, as estimated by the actuary, of the total liability of the retirement system on account of payments which the retirement system may be required to make to any other fund without a corresponding offset in the liabilities of the retirement system.

         (a-1)   Notwithstanding any other provision of law to the contrary, for the purpose of calculating the amount of the normal contribution due from the city to the contingent reserve fund pursuant to subparagraph (c) of this paragraph in fiscal year two thousand five-two thousand six, and in each fiscal year thereafter, both the total liability of the retirement system, as calculated by the actuary in accordance with subparagraph (a) of this paragraph, and the normal rate of contributions, as calculated by the actuary in accordance with subparagraph (b) of this paragraph, shall be determined as of June thirtieth of the second fiscal year preceding the fiscal year in which the normal contribution is payable, provided, however, that (i) the actuary shall use for such calculations the mortality and other tables that are applicable at the time he or she performs such calculations; (ii) the total funds on hand, as determined by the actuary pursuant to sub-item (E) of item (i) of subparagraph (b) of this paragraph, shall be adjusted by adding to such amount the present value of all employer contributions required to be paid into the contingent reserve fund in the fiscal year next preceding the fiscal year in which the normal contribution is payable, as determined by the actuary; and (iii) the present value of the prospective future salaries of all members, as computed by the actuary for the purposes of item (ii) of subparagraph (b) of this paragraph, shall be reduced by the present value of the salaries expected to be paid to all members in the fiscal year next preceding the fiscal year in which the normal contribution is payable, as determined by the actuary.

         (b)   The normal rate of contribution shall be the rate per centum obtained:

            (i)   by deducting from the amount of such total liability the sum of:

               (A)   (1)   the amount obtained by adding together the present value of all required future revised unfunded accrued liability contributions and the present value of all required future payments of the nineteen hundred eighty unfunded accrued liability adjustment, determined pursuant to subparagraph (c) of paragraph three of this subdivision, if such adjustment is a charge; or

                  (2)   the remainder obtained by subtracting from the present value of all required future revised unfunded accrued liability contributions, the present value of all future installments of the nineteen hundred eighty unfunded accrued liability adjustment required to be credited, if such nineteen hundred eighty adjustment is a credit;

                  (3)   minus (whether (1) or (2) of this sub-item (A) is applicable) the present value of all future installments of the nineteen hundred eighty-two unfunded accrued liability adjustment; and

               (A-1)   the present value of all future installments of the aggregate nineteen hundred eighty-five unfunded accrued liability adjustment determined pursuant to sub-item (K) of item (vii) of subparagraph (c) of paragraph three of this subdivision b; and

               (B)   the present value of all required future balance sheet liability, contributions, plus, in the case of the determination of the normal contributions payable in fiscal year nineteen hundred eighty-nineteen hundred eighty-one, the present value, as of June thirtieth, nineteen hundred eighty, of the payment of interest on the balance sheet liability as required by item (v) of subparagraph (a) of paragraph one of this subdivision; and

               (C)   the present value of all required future payments, pursuant to section 13-704 of this title, of installments of losses in excess of installments of gains on dispositions of securities within the meaning of such section; and

               (D)   in the case of the determination of the normal contribution payable in each fiscal year commencing with fiscal year nineteen hundred ninety-five – nineteen hundred ninety-six, the present value of future member contributions of all members; and

               (E)   the total funds on hand, including the amount of any unpaid moneys appropriated pursuant to section 13-133 of this chapter and, in the case of the determination of the normal contribution payable in each fiscal year commencing with fiscal year nineteen hundred ninety-five – nineteen hundred ninety-six, including the amount in the annuity savings fund; and

               (F)   the present value of all other future installments of accrued liability contributions to the retirement system required by the applicable provisions of section 13-638.2 of this title which are not covered by the preceding subitems of this item (i); and

            (ii)   by dividing the remainder by one per centum of the present value of the prospective future salaries of all members, as computed by the actuary on the basis of the latest mortality and service tables adopted pursuant to section 13-121 of this subchapter, and on the basis of regular interest. The normal rate of contribution determined by the actuary shall not be less than zero, shall be certified by the actuary after each such valuation and shall continue in force until the next succeeding valuation and certification.

         (c)   (i)   The amount of the normal contribution due from the city to the contingent reserve fund in each city fiscal year, commencing with the nineteen hundred eighty-nineteen hundred eighty-one fiscal year and ending with the two thousand four-two thousand five fiscal year, shall be the amount obtained by multiplying the normal rate of contribution, as determined by the actuary as of June thirtieth next preceding such fiscal year, by the aggregate annual salaries of the members on such next preceding June thirtieth, and shall be payable in such fiscal year next following such June thirtieth, together with such regular interest thereon which may be due, if any, as calculated by the actuary.

            (ii)   The amount of the normal contribution due from the city to the contingent reserve fund in each city fiscal year, commencing with the two thousand five-two thousand six fiscal year, shall be the amount obtained by multiplying the normal rate of contribution, as determined by the actuary as of the second June thirtieth preceding the fiscal year in which the normal contribution is payable, in accordance with the provisions of subparagraphs (a-1) and (b) of this paragraph, by the aggregate amount of the salaries expected to be paid to the members during the fiscal year in which the normal contribution is payable, as determined by the actuary, and such normal contribution shall be payable in the second fiscal year following the June thirtieth as of which the normal rate of contribution is determined, together with such regular interest thereon which may be due, if any, as calculated by the actuary.

            (iii)   In the case of the normal contribution payable in the nineteen hundred eighty-nineteen hundred eighty-one fiscal year and in any subsequent fiscal year, the term "regular interest", as used in this subparagraph, shall mean regular interest as defined by the applicable provisions of subparagraph (ii) or subparagraph (iii) of paragraph (c) or paragraph (d) of subdivision twelve of section 13-101 of this chapter.

         (d)   (i)   Notwithstanding the preceding subparagraphs of this paragraph or any other provision of law to the contrary, the normal contribution payable to the contingent reserve fund in fiscal year two thousand eleven – two thousand twelve, and in each fiscal year thereafter, shall be the entry age normal contribution, as determined by the actuary pursuant to this subparagraph in a manner consistent with the entry age actuarial cost method. The actuary shall determine the entry age normal contribution for each such fiscal year as of June thirtieth of the second fiscal year preceding the fiscal year in which such normal contribution is payable, based on the latest mortality and other tables applicable at the time he or she performs such calculations, and the valuation rate of interest as provided for the retirement system in paragraph two of subdivision b of section 13-638.2 of this title.

            (ii)   In calculating the entry age normal contribution payable in any such fiscal year pursuant to this subparagraph, the actuary, in his or her discretion, may make certain adjustments in the calculation methodology, provided that such adjustments are generally accepted as consistent with the entry age actuarial cost method, and are designed, in general, to fund, on a level basis over the working lifetimes of members from their ages at entry, the actuarial present value of benefits to which such members are expected to become entitled, as determined by the actuary. Such generally accepted adjustments in the calculation methodology, in the discretion of the actuary, may include, but are not limited to, the calculation of the entry age normal contribution (A) on an individual member basis by calculating the amount of the entry age normal contribution attributable to each individual member, and then adding together such individual member amounts, (B) on an aggregate basis for all members or (C) on any combination of an individual member basis and an aggregate basis which is consistent with the entry age actuarial cost method, and the preceding provisions of this item.

            (iii)   For each such fiscal year, the actuary, in his or her discretion, shall determine, in accordance with the provisions of item (ii) of this subparagraph, the methodology for calculating the entry age normal contribution payable for that particular fiscal year.

            (iv)   The methodology determined by the actuary in accordance with item (iii) of this subparagraph may provide for the actuary to calculate the entry age normal contribution on an individual member basis by (A) multiplying the entry age normal contribution rate for each individual member, as determined by the actuary, by the salary expected to be paid to that member during the fiscal year in which such normal contribution is payable, and (B) calculating the sum of the individual entry age normal contributions attributable to all such members. The actuary, in his or her discretion, may make any adjustments to such methodology for determining the entry age normal contribution on an individual basis which he or she deems appropriate, and which are consistent with the provisions of item (ii) of this subparagraph.

            (v)   In the alternative, the methodology determined by the actuary in accordance with item (iii) of this subparagraph may provide for the actuary to calculate the entry age normal contribution on an aggregate basis by multiplying the entry age normal contribution rate for all members in the aggregate, as determined by the actuary, by the aggregate amount of the salaries expected to be paid to all members during the fiscal year in which the normal contribution is payable. The actuary, in his or her discretion, may make any adjustments to such methodology for determining the entry age normal contribution on an aggregate basis which he or she deems appropriate, and which are consistent with the provisions of item (ii) of this subparagraph.

            (vi)   In the alternative, the methodology determined by the actuary in accordance with item (iii) of this subparagraph may provide for the calculation of the entry age normal contribution on any other basis which the actuary deems appropriate, and which is consistent with the entry age actuarial cost method and the provisions of item (ii) of this subparagraph.

            (vii)   (A)   Where the methodology determined by the actuary in accordance with item (iii) of this subparagraph requires the determination of an entry age normal contribution rate for each individual member in order to calculate the entry age normal contribution for each individual member, the actuary shall determine such rate for each such member in accordance with the entry age actuarial cost method, and such rate, as determined by the actuary for each such member, shall be consistent with a method designed, in general, to fund, on a level basis over the working lifetime of that particular member from his or her age at entry, the actuarial present value of benefits to which such member is expected to become entitled, as determined by the actuary.

               (B)   Where the methodology determined by the actuary in accordance with item (iii) of this subparagraph requires the determination of an entry age normal contribution rate for all members in the aggregate in order to calculate the entry age normal contribution for all members in the aggregate, the actuary shall determine such rate in accordance with the entry age actuarial cost method, and such rate, as determined by the actuary, shall be consistent with a method designed, in general, to fund, on a level basis over the working lifetimes of members from their ages at entry, the actuarial present value of benefits to which such members are expected to become entitled, as determined by the actuary.

      (3)   Unfunded accrued liability contributions.

         (a)   The original unfunded accrued liability contribution shall be an amount which, if paid to the contingent reserve fund in forty equal annual installments, commencing with payment of a first installment in the city's nineteen hundred seventy-seven-nineteen hundred seventy-eight fiscal year, would be the actuarial equivalent, on the basis of five and one-half per centum interest and the actuarial tables in effect as of July first, nineteen hundred seventy-seven, of the difference between the accrued liability excluding the liability for benefits attributable to the annuity savings fund on June thirtieth, nineteen hundred seventy-five and the total funds on hand, excluding the amount in the annuity savings fund, but including the amount of any unpaid moneys appropriated pursuant to section 13-133 of this chapter. The original unfunded accrued liability contributions shall include the payments required by section 13-130 of this chapter.

         (b)   (i)   The revised unfunded accrued liability contribution shall be an amount determined as prescribed in items (ii), (iii), (iv), (v), (vi) and (vii) of this subparagraph (b).

            (ii)   To the amount of the difference constituting the unfunded accrued liability as of June thirtieth, nineteen hundred seventy-five heretofore determined pursuant to the provisions of this paragraph as in effect on July first, nineteen hundred seventy-seven, there shall be added interest thereon at the rate of five and one-half per centum per annum for the period from July first, nineteen hundred seventy-five to June thirtieth, nineteen hundred eighty.

            (iii)   (A)   There shall be computed, in the manner provided in sub-item (B) of this item, the discounted value of each of the installments of the unfunded accrued liability contribution which, in the absence of the enactment of chapter nine hundred fifty-seven of the laws of nineteen hundred eighty-one, were payable or would have been payable in the city's nineteen hundred seventy-seven-nineteen hundred seventy-eight, nineteen hundred seventy-eight-nineteen hundred seventy-nine, nineteen hundred seventy-nine-nineteen hundred eighty, nineteen hundred eighty-nineteen hundred eighty-one and nineteen hundred eighty-one-nineteen hundred eighty-two fiscal years.

               (B)   Such discounted value of each such installment shall be computed as of January first of the city's second fiscal year preceding the fiscal year in which such installment was payable or would have been payable and on the basis of five and one-half per centum interest per annum on the amount of such installment.

               (C)   There shall be computed with respect to such discounted value of each such installment, interest thereon from January first of such second fiscal year preceding the fiscal year in which such installment was or would have been payable to June thirtieth, nineteen hundred eighty at the rate of five and one-half per centum per annum.

               (D)   The discounted values of all of such installments with respect to such fiscal years, computed as provided for in sub-items (A) and (B) of this item, together with interest on each installment as provided for in sub-item (C) of this item, shall be added together.

            (iv)   From the sum computed pursuant to item (ii) of this subparagraph, the sum computed pursuant to item (iii) of this subparagraph shall be subtracted.

            (v)   With respect to each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty and ending on June thirtieth, nineteen hundred eighty-two, the revised unfunded accrued liability contribution shall be the annual installment, applicable to such fiscal year, of an amount which, if paid to the contingent reserve fund in thirty-five equal annual installments, commencing with payment of a first installment in the city's nineteen hundred eighty-nineteen hundred eighty-one fiscal year, would be the actuarial equivalent, on the basis of seven and one-half per centum interest per annum, of the remainder computed pursuant to item (iv) of this subparagraph.

            (vi)   With respect to each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-two and ending on June thirtieth, nineteen hundred eighty-eight, the revised unfunded accrued liability contribution shall be the annual installment, applicable to such fiscal year, of an amount which, if paid to the contingent reserve fund in thirty-three equal annual installments, commencing with payment of a first installment in the city's nineteen hundred eighty-two-nineteen hundred eighty-three fiscal year, would be the actuarial equivalent, on the basis of eight per centum interest per annum, of the present value, as of June thirtieth, nineteen hundred eighty-two on the basis of seven and one-half per centum interest per annum, of the installments of the unfunded accrued liability contribution computed pursuant to item (v) of this subparagraph, which installments are hypothetically allocated by such item (v) to designated city fiscal years succeeding June thirtieth, nineteen hundred eighty-two.

            (vii)   With respect to each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-eight and ending on June thirtieth, two thousand fifteen, the revised unfunded accrued liability contribution shall be the annual installment, applicable to such fiscal year, of an amount which, when paid to the contingent reserve fund in twenty-seven equal annual installments, commencing with payment of a first installment in the city's nineteen hundred eighty-eight-nineteen hundred eighty-nine fiscal year, shall be the actuarial equivalent, on the basis of eight and one-quarter per centum interest per annum, of the present value, as of June thirtieth, nineteen hundred eighty-eight on the basis of eight per centum interest per annum, of the installments of the unfunded accrued liability contribution computed pursuant to item (vi) of this subparagraph, which installments are hypothetically allocated by such item (vi) to designated city fiscal years succeeding June thirtieth, nineteen hundred eighty-eight.

         (c)   (i)   The nineteen hundred eighty unfunded accrued liability adjustment shall be an amount determined as prescribed in items (ii), (iii), (iv) and (v) of this subparagraph.

            (ii)   (A)   Upon the basis of the actuarial tables in effect as of June thirtieth, nineteen hundred eighty for valuation purposes and interest at the rate of seven and one-half per centum per annum, there shall be determined, as of June thirtieth, nineteen hundred eighty, the amount of the total liability for all benefits provided in this chapter, in articles eleven and fourteen of the retirement and social security law and in any other law prescribing benefits payable by the retirement system on account of all members and beneficiaries, excluding the liability on account of future increased-take-home-pay contributions, if any, and the liability for benefits attributable to the annuity savings fund.

               (B)   From such total liability computed pursuant to sub-item (A) of this item, there shall be subtracted the sum of:

                  (1)   the present value, as of June thirtieth, nineteen hundred eighty, of all future normal costs of the retirement system, computed pursuant to the entry age normal cost method of determining such normal costs; and

                  (2)   the present value, as of such June thirtieth, of all future installments of the balance sheet liability contribution (as defined in paragraph four of this subdivision b); and

                  (3)   the present value, as of such June thirtieth, of all then required future payments, pursuant to section 13-704 of this title, of installments of losses in excess of installments of gains on dispositions of securities within the meaning of such section; and

                  (4)   the present value, as of such June thirtieth, of future member contributions of members subject to article fourteen of the retirement and social security law; and

                  (5)   the total funds on hand as of such June thirtieth, excluding the amount in the annuity savings fund, but including the amount of any unpaid moneys appropriated pursuant to section 13-133 of this chapter.

            (iii)   (A)   If the amount computed pursuant to sub-item (B) of item (ii) of this subparagraph is larger than the amount computed pursuant to item (iv) of subparagraph (b) of this paragraph, the latter amount shall be subtracted from the former amount and the remainder resulting from such subtraction shall constitute a charge.

               (B)   If the amount computed pursuant to sub-item (B) of item (ii) of this subparagraph is smaller than the amount computed pursuant to item (iv) of subparagraph (b) of this paragraph, the former amount shall be subtracted from the latter amount and the remainder resulting from such subtraction shall constitute a credit.

            (iv)   (A)   If the remainder computed pursuant to item (iii) of this subparagraph is a charge, the nineteen hundred eighty unfunded accrued liability adjustment shall be an amount which, if paid to the contingent reserve fund in thirty equal annual installments, commencing with payment of a first installment in the city's nineteen hundred eighty-nineteen hundred eighty-one fiscal year, would be the actuarial equivalent, on the basis of seven and one-half per centum interest per annum, of such remainder.

               (B)   If the remainder computed pursuant to item (iii) of this subparagraph is a credit, the nineteen hundred eighty unfunded accrued liability adjustment shall be an amount which, if credited in thirty equal annual installments (the first of which installments is to be credited in the city's nineteen hundred eighty-nineteen hundred eighty-one fiscal year) in reduction of the amounts which the city (and other obligors required to pay public employer contributions on account of members) would otherwise be required to pay to the contingent reserve fund pursuant to items (i), (iii), (iv), (v), (vi) and (vii) of subparagraph (a) of paragraph one of this subdivision or otherwise pursuant to law, would be the actuarial equivalent, on the basis of seven and one-half per centum interest per annum, of such remainder.

            (v)   (A)   With respect to determination of the amount of contributions payable to the contingent reserve fund in each of the city's nineteen hundred eighty-nineteen hundred eighty-one and nineteen hundred eighty-one-nineteen hundred eighty-two fiscal years, the annual installment of the nineteen hundred eighty unfunded accrued liability adjustment computed pursuant to item (iv) of this subparagraph, which installment is applicable to such fiscal year, shall be applied as a charge or a credit, as the case may be, in relation to such contributions payable in such fiscal year.

               (B)   With respect to determination of the amount of contributions payable to the contingent reserve fund in each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-two and ending on June thirtieth, nineteen hundred eighty-eight, the nineteen hundred eighty unfunded accrued liability adjustment shall be an amount which, if paid (if a charge) or credited (if a credit) in twenty-eight equal annual installments, commencing with a payment or credit, as the case may be, in the city's nineteen hundred eighty-two-nineteen hundred eighty-three fiscal year, would be the actuarial equivalent, on the basis of eight per centum interest per annum, of the present value, as of June thirtieth, nineteen hundred eighty-two on the basis of seven and one-half per centum interest per annum, of those installments of the nineteen hundred eighty unfunded accrued liability adjustment computed pursuant to item (iv) of this subparagraph, which installments are hypothetically allocated by such item (iv) to designated city fiscal years succeeding June thirtieth, nineteen hundred eighty-two.

               (C)   With respect to determination of the amount of contributions payable to the contingent reserve fund in each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-eight and ending on June thirtieth, two thousand ten, the nineteen hundred eighty unfunded accrued liability adjustment shall be an amount which, when paid (if a charge) or credited (if a credit) in twenty-two equal annual installments, commencing with a payment or credit, as the case may be, in the city's nineteen hundred eighty-eight-nineteen hundred eighty-nine fiscal year, shall be the actuarial equivalent, on the basis of eight and one-quarter per centum interest per annum, of the present value, as of June thirtieth, nineteen hundred eighty-eight on the basis of eight per centum interest per annum, of those installments of the nineteen hundred eighty unfunded accrued liability adjustment computed pursuant to sub-item (B) of this item (v), which installments are hypothetically allocated by such sub-item (B) to designated city fiscal years succeeding June thirtieth, nineteen hundred eighty-eight.

               (D)   With respect to determination of the amount of contributions payable to the contingent reserve fund in each of such city fiscal years referred to in sub-item (B) of sub-item (C) of this item, the annual installment of the nineteen hundred eighty unfunded accrued liability adjustment computed pursuant to sub-item (B) or sub-item (C) of this item, which installment is applicable to such fiscal year, shall be applied as a charge or credit, as the case may be, in relation to such contributions payable in such fiscal year.

            (vi)   (A)   The nineteen hundred eighty-two unfunded accrued liability adjustment shall be an amount determined as prescribed in sub-items (B), (C), (D) and (E) of this item.

               (B)   Upon the basis of the actuarial tables in effect as of June thirtieth, nineteen hundred eighty-one for valuation purposes and interest at the rate of seven and one-half per centum per annum, there shall be determined, as of June thirtieth, nineteen hundred eighty-two, the amount of the actuarial accrued liability of the retirement system, computed pursuant to the entry age normal cost method of ascertaining such actuarial accrued liability.

               (C)   Upon the basis of the actuarial tables in effect as of June thirtieth, nineteen hundred eighty-two for valuation purposes and interest at the rate of eight per centum per annum, there shall be determined, as of June thirtieth, nineteen hundred eighty-two, the amount of the actuarial accrued liability of the retirement system, computed pursuant to the entry age normal cost method of ascertaining such actuarial accrued liability.

               (D)   With respect to determination of the amount of contributions payable to the contingent reserve fund in such city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-two and ending on June thirtieth, nineteen hundred eighty-eight, the nineteen hundred eighty-two unfunded accrued liability adjustment shall be an amount which, if credited in thirty equal annual installments (the first of which installments is to be credited in the city's nineteen hundred eighty-two-nineteen hundred eighty-three fiscal year) in reduction of the amounts which the city (and other obligors required to pay public employer contribution on account of members) would otherwise be required to pay to the contingent reserve fund pursuant to items (i), (iii), (iv), (vi) and (vii) of subparagraph (a) of paragraph (1) of this subdivision b or otherwise pursuant to law, would be the actuarial equivalent, on the basis of eight per centum interest per annum, of the excess of the amount computed pursuant to sub-item (B) of this item (vi) over the amount computed pursuant to sub-item (C) of this item (vi).

               (E)   With respect to determination of the amount of contributions payable to the contingent reserve fund in each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-eight and ending on June thirtieth, two thousand twelve, the nineteen hundred eighty-two unfunded accrued liability adjustment shall be an amount which, when credited in twenty-four equal annual installments (the first of which installments is to be credited in the city's nineteen hundred eighty-eight-nineteen hundred eighty-nine fiscal year) in reduction of the amounts which the city (and other obligors required to pay public employer contribution on account of members) would otherwise be required to pay to the contingent reserve fund pursuant to items (i), (iii), (iv), (vi) and (vii) of subparagraph (a) of paragraph (1) of this subdivision b or otherwise pursuant to law, shall be the actuarial equivalent, on the basis of eight and one-quarter per centum interest per annum, of the present value, as of June thirtieth, nineteen hundred eighty-eight on the basis of eight per centum interest per annum, of those installments of the nineteen hundred eighty-two unfunded accrued liability adjustment computed pursuant to sub-item (D) of this item (vi), which installments are hypothetically allocated by such sub-item (D) to designated city fiscal years succeeding June thirtieth, nineteen hundred eighty-eight.

            (vii)   (A)   With respect to any obligor required by law to make contributions to the contingent reserve fund, the nineteen hundred eighty-five unfunded accrued liability adjustment shall be an amount determined for such obligor as prescribed by the applicable provisions of the succeeding sub-items of this item (vii).

               (B)   Upon the basis of the actuarial tables in effect for valuation purposes with respect to determination of the normal contribution payable to the contingent reserve fund in the city's nineteen hundred eighty-four-nineteen hundred eighty-five fiscal year and interest at the rate of eight per centum per annum, there shall be determined, as of June thirtieth, nineteen hundred eighty-five, the amount of the actuarial accrued liability of the retirement system, computed pursuant to the entry age normal cost method of ascertaining such actuarial accrued liability.

               (C)   Upon the basis of the actuarial tables in effect for valuation purposes with respect to determination of the normal contribution payable to the contingent reserve fund in the city's nineteen hundred eighty-five-nineteen hundred eighty-six fiscal year and interest at the rate of eight per centum per annum, there shall be determined, as of June thirtieth, nineteen hundred eighty-five, the amount of the actuarial accrued liability of the retirement system, computed pursuant to the entry age normal cost method of ascertaining such actuarial accrued liability.

               (D)   The actuary shall determine the portion of the liability (other than liability on account of the senior colleges of the city university) computed pursuant to sub-item (B) of this item (vii), which portion is attributable to each obligor required by law to make contributions to the contingent reserve fund of the retirement system.

               (E)   The actuary shall determine the portion of the liability (other than liability on account of such senior colleges) computed pursuant to sub-item (C) of this item (vii), which portion is attributable to each such obligor.

               (F)   If the portion computed pursuant to sub-item (E) of this item (vii) with respect to any such obligor is greater than the portion computed pursuant to sub-item (D) of this item (vii) with respect to such obligor, the nineteen hundred eighty-five unfunded accrued liability adjustment with respect to such obligor for each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-five and ending on June thirtieth, nineteen hundred eighty-eight, shall be the annual installment applicable to such fiscal year of a charge in an amount which, if paid by such obligor to the contingent reserve fund in thirty equal annual installments, commencing with payment of a first installment in the city's nineteen hundred eighty-five-nineteen hundred eighty-six fiscal year, would be the actuarial equivalent, on the basis of eight per centum interest per annum, of the excess of the amount of such portion computed pursuant to sub-item (E) of this item (vii) over the amount of such portion, computed pursuant to sub-item (D) of this item (vii).

               (F-1)   If the portion computed pursuant to sub-item (E) of this item (vii) with respect to any such obligor is greater than the portion computed pursuant to sub-item (D) of this item (vii) with respect to such obligor, the nineteen hundred eighty-five unfunded accrued liability adjustment with respect to such obligor for each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-eight and ending on June thirtieth, two thousand fifteen, shall be the annual installment applicable to such fiscal year of a charge in an amount which, when paid by such obligor to the contingent reserve fund in twenty-seven equal annual installments, commencing with payment of a first installment in the city's nineteen hundred eighty-eight-nineteen hundred eighty-nine fiscal year, shall be the actuarial equivalent, on the basis of eight and one-quarter per centum interest per annum, of the present value, as of June thirtieth, nineteen hundred eighty-eight on the basis of eight per centum interest per annum, of the installments of unfunded accrued liability adjustment computed pursuant to sub-item (F) of this item (vii), which installments are hypothetically allocated by such sub-item (F) to designated city fiscal years succeeding June thirtieth, nineteen hundred eighty-eight.

               (G)   If the portion computed pursuant to sub-item (D) of this item (vii) with respect to any such obligor is greater than the portion computed pursuant to sub-item (E) of this item (vii) with respect to such obligor, the nineteen hundred eighty-five unfunded accrued liability adjustment with respect to such obligor for each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-five and ending on June thirtieth, nineteen hundred eighty-eight, shall be the annual installment applicable to such fiscal year of a credit in an amount which, if credited in thirty equal annual installments, (the first of which installments is to be credited in the city's nineteen hundred eighty-five-nineteen hundred eighty-six fiscal year) in reduction of the amounts which such obligor would otherwise be required to pay to the contingent reserve fund pursuant to items (i), (iii), (iv), (v), (vi) and (vii) of subparagraph (a) of paragraph one of this subdivision b or otherwise pursuant to law, would be the actuarial equivalent, on the basis of eight per centum interest per annum, of the excess of the amount of such portion computed pursuant to sub-item (D) of this item (vii) over the amount of such portion computed pursuant to sub-item (E) of this item (vii).

               (G-1)   If the portion computed pursuant to sub-item (D) of this item (vii) with respect to any such obligor is greater than the portion computed pursuant to sub-item (E) of this item (vii) with respect to such obligor, the nineteen hundred eighty-five unfunded accrued liability adjustment with respect to such obligor for each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-eight and ending on June thirtieth, two thousand fifteen, shall be a credit in an amount which, when credited in twenty-seven equal annual installments, (the first of which installments is to be credited in the city's nineteen hundred eighty-eight-nineteen hundred eighty-nine fiscal year) in reduction of the amounts which such obligor would otherwise be required to pay to the contingent reserve fund pursuant to items (i), (iii), (iv), (v), (vi) and (vii) of subparagraph (a) of paragraph one of this subdivision b or otherwise pursuant to law, shall be the actuarial equivalent, on the basis of eight and one-quarter per centum interest per annum, of the present value, as of June thirtieth, nineteen hundred eighty-eight on the basis of eight per centum interest per annum, of those installments of the unfunded accrued liability adjustment computed pursuant to sub-item (G) of this item (vii), which installments are hypothetically allocated by such sub-item (G) to designated city fiscal years succeeding June thirtieth, nineteen hundred eighty-eight.

               (H)   The actuary shall determine the portion of the liability computed pursuant to sub-item (B) of this item (vii), which portion is attributable to the senior colleges of the city university of New York.

               (I)   The actuary shall determine the portion of the liability computed pursuant to sub-item (C) of this item (vii), which portion is attributable to such senior colleges.

               (J)   With respect to each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-five and ending on June thirtieth, nineteen hundred eighty-eight, the nineteen hundred eighty-five unfunded accrued liability adjustment attributable to the senior colleges of such university shall be the annual installment applicable to such fiscal year of an amount which, if credited in thirty equal annual installments (the first of which installments is to be credited in the city's nineteen hundred eighty-five-nineteen hundred eighty-six fiscal year) in reduction of the amounts which the city and/or the state of New York would otherwise be required to pay to the contingent reserve fund pursuant to items (i), (iii), (iv), (v), (vi) and (vii) of subparagraph (a) of paragraph one of this subdivision b or otherwise pursuant to law, would be the actuarial equivalent, on the basis of eight per centum interest per annum, of the excess of the amount of such portion computed pursuant to sub-item (H) of this item (vii) over the amount of such portion computed pursuant to sub-item (I) of this item (vii).

               (J-1)   With respect to each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-eight and ending on June thirtieth, two thousand fifteen, the nineteen hundred eighty-five unfunded accrued liability adjustment attributable to the senior colleges of such university shall be the annual installment applicable to such fiscal year of an amount which, when credited in twenty-seven equal annual installments (the first of which installments is to be credited in the city's nineteen hundred eighty-eight-nineteen hundred eighty-nine fiscal year) in reduction of the amounts which the city and/or the state of New York would otherwise be required to pay to the contingent reserve fund pursuant to items (i), (iii), (iv), (v), (vi) and (vii) of subparagraph (a) of paragraph one of this subdivision b or otherwise pursuant to law, shall be the actuarial equivalent, on the basis of eight and one-quarter per centum interest per annum, of the present value, as of June thirtieth, nineteen hundred eighty-eight on the basis of eight per centum interest per annum, of those installments of the unfunded accrued liability adjustment computed pursuant to sub-item (J) of this item (vii), which installments are hypothetically allocated by such sub-item (J) to designated city fiscal year succeeding June thirtieth, nineteen hundred eighty-eight.

               (K)   With respect to each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-five and ending on June thirtieth, nineteen hundred eighty-eight, the aggregate nineteen hundred eighty-five unfunded accrued liability adjustment shall be the annual installment applicable to such fiscal year of an amount, which, if paid to the contingent reserve fund in thirty equal annual installments, commencing with payment of a first installment in the city's nineteen hundred eighty-five-nineteen hundred eighty-six fiscal year, would be the actuarial equivalent, on the basis of eight per centum interest per annum, of the excess of the amount computed pursuant to sub-item (C) of this item (vii) over the amount computed pursuant to sub-item (B) of this item (vii).

               (K-1)   With respect to each city fiscal year occurring during the period beginning on July first, nineteen hundred eighty-eight and ending June thirtieth, two thousand fifteen, the aggregate nineteen hundred eighty-five unfunded accrued liability adjustment shall be the annual installment applicable to such fiscal year of an amount, which, when paid to the contingent reserve fund in twenty-seven equal annual installments, commencing with payment of a first installment in the city's nineteen hundred eighty-eight-nineteen hundred eighty-nine fiscal year, shall be the actuarial equivalent, on the basis of eight and one-quarter per centum interest per annum, of the present value, as of June thirtieth, nineteen hundred eighty-eight on the basis of eight per centum interest per annum, of those installments of the unfunded accrued liability adjustment computed pursuant to sub-item (K) of this item (vii), which installments are hypothetically allocated by such sub-item (K) to designated city fiscal years succeeding June thirtieth, nineteen hundred eighty-eight.

      (4)   (a)   As used in this section, the following words and phrases, unless a different meaning is plainly required by the context, shall have the following meanings:

            (i)   (A)   "Normal contribution for balance sheet liability purposes". The hypothetical amount which the normal contribution payable in each city fiscal year occurring during the period beginning on July first, nineteen hundred seventy-four and ending on June thirtieth, nineteen hundred eighty would have equalled if such normal contribution had been required by law to be paid to the contingent reserve fund in the city fiscal year in which the obligation to make such normal contribution accrued and such normal contribution had been required by law to be determined in the manner provided for in sub-items (B), (C) and (D) of this item (i).

               (B)   Upon the basis of the mortality and other tables effective under this chapter as of July first, nineteen hundred seventy-seven and interest at the rate of five and one-half per centum per annum, the actuary shall determine, as of June thirtieth next preceding each such fiscal year for which such normal contribution is being determined (hereinafter referred to as the "subject fiscal year") the amount of the then total liability for all benefits provided in this chapter, in articles eleven and fourteen of the retirement and social security law and in any other law prescribing benefits payable by the retirement system on account of all then members and beneficiaries, excluding the then liability on account of future annual contributions, for balance sheet liability purposes, on account of reserves-for-increased-take-home-pay (as defined in item (iv) of this subparagraph (a), if any, and the then liability for benefits attributable to the annuity savings fund.

               (C)   The hypothetical normal rate of contribution with respect to the subject fiscal year shall be the rate per centum obtained:

                  (i)   by deducting from the amount of such total liability the sum of:

                     (A)   the present value of all then required future unfunded accrued liability contributions for balance sheet liability purposes (as defined in item (ii) of this subparagraph (a)); and

                     (B)   the present value of all then required future annual contributions, for balance sheet liability purposes, on account of amortization of losses on dispositions of certain securities within the meaning of section 13-704 of this title (as defined in item (iii) of this subparagraph (a)); and

                     (C)   the present value of future member contributions of members subject to article fourteen of the retirement and social security law; and

                     (D)   the amount obtained by adding together the total funds on hand (excluding therefrom the amount in the annuity savings fund) and the balance sheet liability as of such June thirtieth next preceding the subject fiscal year; and

                  (ii)   by dividing the remainder by one per centum of the then present value of the prospective future salaries of all members, as computed on the basis of the mortality and service tables adopted pursuant to section 13-121 of this chapter and in effect on July first, nineteen hundred seventy-seven, and on the basis of interest at the rate of five and one-half per centum per annum.

               (D)   The amount of the normal contribution for balance sheet liability purposes hypothetically payable in the subject fiscal year shall be the amount obtained (1) by multiplying such hypothetical normal contribution rate computed with respect to the subject fiscal year by the aggregate annual salaries of the members as of June thirtieth of the subject fiscal year and (2) by adding to the product of such multiplication, interest on such product at the rate of five and one-half per centum per annum for a period of six months.

            (ii)   "Unfunded accrued liability contribution for balance sheet liability purposes".

               (A)   With respect to the city's nineteen hundred seventy-four-nineteen hundred seventy-five fiscal year, such term shall mean a hypothetical amount which, if paid to the contingent reserve fund in forty equal annual installments, beginning with payment of a first installment in the city's nineteen hundred seventy-four-nineteen hundred seventy-five fiscal year, would be the actuarial equivalent, on the basis of interest at the rate of five and one-half per centum per annum, of the remainder computed in the manner prescribed by sub-items (B) and (C) of this item (ii).

               (B)   Upon the basis of the actuarial tables in effect as of July first, nineteen hundred seventy-seven for valuation purposes and interest at the rate of five and one-half per centum per annum, there shall be computed, as of June thirtieth, nineteen hundred seventy-four, the amount of the total liability for all benefits provided by this title, in article eleven of the retirement and social security law and in any other law prescribing benefits payable by the retirement system on account of all members and beneficiaries, excluding the liability on account of future increased-take-home-pay contributions and the liability for benefits attributable to the annuity savings fund.

               (C)   From such total liability computed pursuant to sub-item (B) of this item (ii) there shall be subtracted the sum of:

                  (1)   the present value, as of June thirtieth, nineteen hundred seventy-four, of all future normal costs of the retirement system, computed pursuant to the entry age normal cost method of determining such normal costs; and

                  (2)   the present value, as of such June thirtieth, of all then required future payments, pursuant to section 13-704 of this title (as then in effect), of installments of losses in excess of installments of gains on dispositions of securities within the meaning of such section; and

                  (3)   the sum obtained by adding together the balance sheet liability as of such June thirtieth, (as such liability is determined pursuant to the provisions of subparagraph (b) of this paragraph four) and the total funds on hand as of such June thirtieth, excluding the amount in the annuity savings fund, but including the amount of any unpaid moneys appropriated pursuant to section 13-133 of this chapter.

               (D)   With respect to each of the city's fiscal years occurring during the period from July first, nineteen hundred seventy-five to June thirtieth, nineteen hundred eighty, such term shall mean a hypothetical amount which, if paid to the contingent reserve fund in forty equal annual installments, beginning with payment of a first installment in the city's nineteen hundred seventy-five-nineteen hundred seventy-six fiscal year, would be the actuarial equivalent, on the basis of interest at the rate of five and one-half per centum per annum, of the remainder computed pursuant to sub-items (E) and (F) of this item (ii).

               (E)   Upon the basis of the actuarial tables in effect as of July first, nineteen hundred seventy-seven for valuation purposes and interest at the rate of five and one-half per centum per annum, there shall be computed, as of June thirtieth, nineteen hundred seventy-five, the amount of the total liability for all benefits provided by this chapter, in article eleven of the retirement and social security law and in any other law prescribing benefits payable by the retirement system on account of all members and beneficiaries, excluding the liability on account of future increased-take-home-pay contributions and the liability for benefits attributable to the annuity savings fund.

               (F)   From such total liability computed pursuant to sub-item (E) of this item (ii), there shall be subtracted the sum of:

                  (1)   the present value, as of June thirtieth, nineteen hundred seventy-five, of all future normal costs of the retirement system, computed pursuant to the entry age normal cost method of determining such normal costs; and

                  (2)   the present value, as of such June thirtieth, of all then required future payments, pursuant to section 13-704 of this title, (as then in effect) of installments of losses in excess of installments of gains on dispositions of securities within the meaning of such section; and

                  (3)   the sum obtained by adding together the balance sheet liability as of such June thirtieth (as such liability is determined pursuant to the provisions of subparagraphs (c) to (i), inclusive, of this paragraph four) and the total funds on hand as of such June thirtieth, excluding the amount in the annuity savings fund, but including the amount of any unpaid moneys appropriated pursuant to section 13-133 of this chapter.

            (iii)   "Annual contribution, for balance sheet liability purposes, on account of amortization of losses on dispositions of certain securities within the meaning of section 13-704 of this title." A hypothetical annual payment to the contingent reserve fund in each of the city's fiscal years occurring during the period beginning on July first, nineteen hundred seventy-four and ending on June thirtieth, nineteen hundred eighty, of the amount of the excess of installments (hypothetically payable in such year) of losses on prior dispositions of securities within the meaning of section 13-704 of this title (relating to graduated crediting of gains and amortization of losses on dispositions of certain securities) over installments (hypothetically creditable in such year) of gains on such prior dispositions, which annual amount shall be determined in the manner provided in subdivision h of section 13-704 of this title.

            (iv)   "Annual contribution, for balance sheet liability purposes, on account of reserves-for-increased-take-home-pay." A hypothetical annual payment to the contingent reserve fund in each of the city's fiscal years occurring during the period from July first, nineteen hundred seventy-four to June thirtieth, nineteen hundred eighty, of the amount required to fulfill the public employer obligation, which accrued in such year, make contributions on account of increased-take-home-pay.

            (v)   "Annual military law contribution for balance sheet liability purposes." A hypothetical annual payment to the contingent reserve fund in each of the city's fiscal years occurring during the period beginning on July first, nineteen hundred seventy-four and ending on June thirtieth, nineteen hundred eighty, of the amount required to fulfill the public employer obligations, which accrued in such year under the provisions of subdivision twenty of section two hundred forty-three of the military law, to pay in behalf of members qualifying for such benefit member contributions with respect to certain periods of military service of such members.

            (vi)   "Deficiency contribution". The total annual amount which, under the provisions of paragraphs one and three of this subdivision and subdivision e of this section (as added by chapter eight hundred twenty-one of the laws of nineteen hundred sixty-eight and amended by chapter eight hundred seventeen of the laws of nineteen hundred sixty-nine), as such provisions were in effect during the period from July first, nineteen hundred seventy-two to June thirtieth, nineteen hundred seventy-seven, the city and other public employers required to contribute as provided for in section 13-130 of this chapter were required to pay to the contingent reserve fund in each of the city's nineteen hundred seventy-four-nineteen hundred seventy-five, nineteen hundred seventy-five-nineteen hundred seventy-six and nineteen hundred seventy-six-nineteen hundred seventy-seven fiscal years.

            (vii)   "Contribution on account of amortization, pursuant to section 13-704 of this title, of losses on dispositions of certain securities". The total annual amount by which the sum of the installments of losses, payable pursuant to section 13-704 of this title (as in effect prior to July first, nineteen hundred eighty) in each of the city's fiscal years occurring during the period from July first, nineteen hundred seventy-four to June thirtieth, nineteen hundred eighty in relation to dispositions of securities within the meaning of such section, exceeded the sum of the installments of gains creditable in the same fiscal year in relation to the same dispositions of securities.

         (b)   The balance sheet liability as of June thirtieth, nineteen hundred seventy-four shall be the sum of six hundred seventy-two million, one hundred eighty-seven thousand, nine hundred seventeen dollars ($672,187,917), consisting of the sum of:

            (i)   The discounted value, as of June thirtieth, nineteen hundred seventy-four of the sum of two hundred seventy-seven million, six hundred eighty-five thousand, nine hundred forty-two dollars ($277,685,942), which constituted the amount payable to the contingent reserve fund in the city's nineteen hundred seventy-four-nineteen hundred seventy-five fiscal year by the city (and other public employers required to contribute as provided for in section 13-130 of this chapter) in fulfillment of their obligations to make contributions to the retirement system payable in such fiscal year, such discounting being calculated on the basis of interest at the rate of five and one-half per centum per annum and a discount period of six months extending retroactively from January first, nineteen hundred seventy-five to June thirtieth, nineteen hundred seventy-four and such discounted value being the sum of two hundred seventy million, three hundred fifty thousand, eight hundred sixty-eight dollars ($270,350,868); and

            (ii)   the discounted value, as of June thirtieth, nineteen hundred seventy-four, of the sum of four hundred thirty-five million, four hundred forty thousand, four hundred twenty-two dollars ($435,440,422), which constituted the amount payable into the contingent reserve fund in the city's nineteen hundred seventy-five-nineteen hundred seventy-six fiscal year by the city (and other public employers required to contribute as provided for in section 13-130 of this chapter) in fulfillment of their obligations to make contributions to the retirement system payable in such fiscal year, such discounting being calculated on the basis of interest at the rate of five and one-half per centum per annum and a discount period of eighteen months extending from January first, nineteen hundred seventy-six retroactively to June thirtieth, nineteen hundred seventy-four, and such discounted value being the sum of four hundred one million, eight hundred thirty-seven thousand, forty-nine dollars ($401,837,049).

         (c)   The balance sheet liability, as of each June thirtieth succeeding June thirtieth, nineteen hundred seventy-four to and including June thirtieth, nineteen hundred eighty, shall be determined as provided for in subparagraphs (d) to (j), inclusive, of this paragraph four.

         (d)   To the amount of the balance sheet liability as of June thirtieth next preceding the June thirtieth (which last-mentioned June thirtieth is hereinafter referred to as the "subject June thirtieth") as of which the balance sheet liability is being determined as provided for in subparagraph (c) of this paragraph four, there shall be added one year's interest on such amount at the rate of five and one-half per centum per annum.

         (e)   With respect to the city's fiscal year ending on the subject June thirtieth (hereinafter referred to as the "subject fiscal year") there shall be added together the contribution components hereinafter specified in this subparagraph (e), which components, for the purposes of this paragraph four, are hypothetically deemed to have accrued in the subject fiscal year and to have been payable therein, as follows:

            (i)   the amount of the normal contribution for balance sheet liability purposes (as defined in item (i) of subparagraph (a) of this paragraph four); and

            (ii)   the amount of the applicable installment of the unfunded accrued liability contribution for balance sheet liability purposes (as defined in item (ii) of subparagraph (a) of this paragraph); and

            (iii)   the amount of the annual contribution, for balance sheet liability purposes, on account of amortization of losses on dispositions of certain securities within the meaning of section 13-704 of this title (as defined in item (iii) of subparagraph (a) of this paragraph); and

            (iv)   the amount of the annual contribution, for balance sheet liability purposes, on account of reserves-for-increased-take-home-pay (as defined in item (iv) of subparagraph (a) of this paragraph); and

            (v)   the amount of the annual military law contribution for balance sheet liability purposes (as defined in item (v) of subparagraph (a) of this paragraph).

         (f)   To the amount resulting from the addition prescribed by subparagraph (e) of this paragraph four, there shall be added interest thereon at the rate of five and one-half per centum per annum from January first of the subject fiscal year to June thirtieth of such fiscal year.

         (g)   The amount computed pursuant to subparagraph (d) of this paragraph four in relation to the balance sheet liability as of June thirtieth next preceding the subject June thirtieth (together with one year's interest on such balance sheet liability) shall be added to the amount computed pursuant to subparagraph (f) of this paragraph in relation to the subject fiscal year.

         (h)   From the amount computed pursuant to subparagraph (g) of this paragraph, there shall be subtracted the sum of:

            (i)   the total amount of the sums paid to the contingent reserve fund during the subject fiscal year by the city (and other obligors required to make public employer contributions to such fund) on account of their obligations which accrued during the city's second fiscal year preceding the subject fiscal year, to provide:

               (A)   the normal contribution payable in the subject fiscal year under the provisions of paragraphs one and two of this subdivision b as then in effect, and

               (B)   the installment of the deficiency contribution (as defined in item (vi) of subparagraph (a) of this paragraph four) or the installment of the original unfunded accrued liability contribution (as defined in subparagraph (a) of paragraph three of this subdivision b), as the case may be, payable in the subject fiscal year; and

               (C)   the amount of the contribution on account of amortization, pursuant to section 13-704 of this title, of losses on dispositions of certain securities (as defined in item (vii) of subparagraph (a) of this paragraph four) payable in the subject fiscal year; and

               (D)   the amount payable in the subject fiscal year on account of reserves-for-increased-take-home-pay; and

               (E)   the amount payable in the subject fiscal year in behalf of members pursuant to subdivision twenty of section two hundred forty-three of the military law; plus

            (ii)   interest on such total amount referred to in item (i) of this subparagraph (h) at the rate of five and one-half per centum per annum from January first of the subject fiscal year to June thirtieth thereof.

         (i)   The remainder resulting from the subtraction prescribed by subparagraph (h) of this paragraph four shall be the balance sheet liability as of June thirtieth of the subject fiscal year.

         (j)   The balance sheet liability as of June thirtieth, nineteen hundred eighty shall be the amount resulting from the successive computations of the balance sheet liability as of each June thirtieth succeeding June thirtieth, nineteen hundred seventy-four up to and including June thirtieth, nineteen hundred eighty, as prescribed by subparagraphs (c) to (i), inclusive, of this paragraph four.

         (k)   (i)   The balance sheet liability contribution payable in the city's nineteen hundred eighty-one-nineteen hundred eighty-two fiscal year shall be the first annual installment of an amount which, if paid to the contingent reserve fund in forty equal annual installments, commencing with payment of a first installment in the city's nineteen hundred eighty-one-nineteen hundred eighty-two fiscal year, would be the actuarial equivalent, as of June thirtieth, nineteen hundred eighty-one, on the basis of seven and one-half per centum interest per annum, of an amount equal to the balance sheet liability as of June thirtieth, nineteen hundred eighty.

            (ii)   The balance sheet liability contribution payable in each city fiscal year during the period beginning on July first, nineteen hundred eighty-two and ending on June thirtieth, nineteen hundred eighty-eight shall be one annual installment of an amount which, if paid to the contingent reserve fund in thirty-nine equal annual installments, commencing with a first payment in the city's nineteen hundred eighty-two-nineteen hundred eighty-three fiscal year, would be the actuarial equivalent, as of June thirtieth, nineteen hundred eighty-two, on the basis of eight per centum interest per annum, of the present value, as of June thirtieth, nineteen hundred eighty-two on the basis of seven and one-half per centum interest per annum, of those installments of the balance sheet liability contribution computed pursuant to item (i) of this subparagraph (k), which installments are hypothetically allocated by such item (i) to designated city fiscal years succeeding June thirtieth, nineteen hundred eighty-two.

            (iii)   The balance sheet liability contribution payable in each city fiscal year during the period beginning on July first, nineteen hundred eighty-eight and ending on June thirtieth, two thousand twenty-one shall be one annual installment of an amount which, when paid to the contingent reserve fund in thirty-three equal annual installments, commencing with a first payment in the city's nineteen hundred eighty-eight-nineteen hundred eighty-nine fiscal year, shall be the actuarial equivalent, as of June thirtieth, nineteen hundred eighty-eight, on the basis of eight and one-quarter per centum interest per annum, of the present value, as of June thirtieth, nineteen hundred eighty-eight on the basis of eight per centum interest per annum, of those installments of the balance sheet liability contribution computed pursuant to item (ii) of this subparagraph (k), which installments are hypothetically allocated by such item (ii) to designated city fiscal years succeeding June thirtieth, nineteen hundred eighty-eight.

      (5)   Contributions to the contingent reserve fund payable in fiscal years of the city beginning on or after July first, nineteen hundred ninety by the city and other obligors required to make such contributions shall be governed by the provisions of this section, as modified and supplemented by section 13-638.2 of this title, and such other laws as may be applicable.

   c.   Whenever the board, upon recommendation by the actuary, shall determine that it is necessary to increase the reserves held in the annuity reserve fund, the pension reserve fund or the pension fund, the board may direct that the amount so needed shall be transferred thereto from the contingent reserve fund.

   d.   (1)   The city shall pay to the contingent reserve fund the accrued additional employer cost of providing the rights, benefits and privileges conferred by section 13-159 of this chapter upon members of the uniformed force of the department of sanitation who elect such rights, benefits and privileges pursuant to subdivision b of such section.

      (2)   Such additional cost shall consist of the amount obtained (a) by computing, as of July second, nineteen hundred sixty-seven, the total of all sums which would have been due, up to and including such date, to the contingent reserve fund with respect to all such members who elect the benefits of such section, if such election by each such member had been authorized by law as provided in subdivision b of such section on the date of his or her appointment as a member of the uniformed force of the department of sanitation, and such election had been made and was in effect on the date on which such member began contributing to the retirement system as a member of such force, and (b) by subtracting from such total mentioned in subparagraph a of this paragraph two, the aggregate of all amounts actually paid in and due to the contingent reserve fund, up to and including July second, nineteen hundred sixty-seven, with respect to all such members making such election.

      (3)   The sums required to be paid by the city to the contingent reserve fund under the provisions of paragraphs one and two of this subdivision shall be computed by the actuary and shall be paid to such fund by the city in equal annual installments over a period of thirty-five years, beginning with the fiscal year of the city commencing on July first, nineteen hundred sixty-nine.

   e.   Upon the retirement of such a member, or upon his or her death in the performance of duty, an amount equal to the pension reserve for the pension payable by the city on account of his or her city-service as a member, together with the reserve-for-increased-take-home-pay, shall be transferred from such fund to the pension reserve fund. Contributions shall be paid into the contingent reserve fund, in the manner and to the extent specified by section 13-152 of this chapter, to provide reserves-for-increased-take-home-pay.

   f.   (1)   The city shall pay to the contingent reserve fund the accrued additional employer cost of providing the rights, benefits and privileges conferred by section 13-159 of this chapter upon sanitation workers who elect such rights, benefits and privileges pursuant to subdivision b of such section.

      (2)   Such additional cost shall consist of the amount obtained (a) by computing, as of July second, nineteen hundred sixty-seven, the total of all sums which would have been due, up to and including such date, to the contingent reserve fund with respect to all such members who elect the benefits of such section, if such election by each such member had been authorized by law as provided in subdivision b of such section on the date of his or her appointment as a sanitation worker, and such election had been made and was in effect on the date on which such member began contributing to the retirement system as a sanitation worker, and (b) by subtracting from such total mentioned in subparagraph a of this paragraph two, the aggregate of all amounts actually paid in and due to the contingent reserve fund, up to and including July second, nineteen hundred sixty-seven, with respect to all such members making such election.

      (3)   The sums required to be paid by the city to the contingent reserve fund under the provisions of paragraphs one and two of this subdivision shall be computed by the actuary and shall be paid to such fund by the city in equal annual installments over a period of thirty-five years, beginning with the fiscal year of the city commencing on July first, nineteen hundred sixty-nine.