(a) multiplying by forty (or forty-three and two-fifths in a case where a retired employee may under this act receive a maximum retirement allowance or pension, computed without optional modification, of thirteen hundred and two dollars) the number of years, not exceeding thirty, of allowable and credited service on which his retirement allowance or pension is based,

(b) subtracting therefrom the amount of his annual retirement allowance or pension, computed without optional modification, and

(c) dividing the results so obtained by twelve. 2. In no event shall the monthly supplemental pension paid to a state retired employee exceed

(a) twenty-five dollars, or thirty-three dollars and fifty cents in any case where the maximum under paragraph (b) of this subdivision is one hundred eight dollars and fifty cents, or

(b) an amount which, when added to an amount equal to one-twelfth of his annual retirement allowance or pension, computed without optional modification, exceeds

(1) the sum of one hundred dollars, or

(2) one hundred eight dollars and fifty cents, in the case of a state retired employee who attained age sixty-five before April first, nineteen hundred fifty-six, or who attains such age on or after such date, beginning with the month of April nineteen hundred fifty-six, if he is then sixty-five years of age or beginning with the month thereafter during which he attains age sixty-five, or who is a female person who attained age sixty-two before April first, nineteen hundred fifty-seven, or who attains such age on or after such date, beginning with the month of April nineteen hundred fifty-seven, if she is then sixty-two years of age or beginning with the month thereafter during which she attains age sixty-two, or is retired for disability, either before or after attaining age fifty, and who attained such age before April first, nineteen hundred fifty-seven, or who attains such age on or after such date, beginning with the month of April nineteen hundred fifty-seven, if he is then fifty years of age or beginning with the month thereafter during which he attains age fifty, or

(3) one hundred eight dollars and fifty cents, in the case of a local retired employee, where the municipality shall have provided by local law, ordinance or resolution for payments up to such sum for local retired employees who attained age sixty-five before April first, nineteen hundred fifty-six, or who attain such age on or after such date, beginning with the month when such local law, ordinance or resolution shall become effective, if such local retired employee is then sixty-five years of age or beginning with the month thereafter during which he attains age sixty-five, or who are female persons who attained age sixty-two before April first, nineteen hundred fifty-seven, or who attain such age on or after such date, beginning with the month when such local law, ordinance or resolution shall become effective, if such local retired employee is then sixty-two years of age or beginning with the month thereafter during which she attains age sixty-two, or who are retired for disability, either before or after attaining age fifty, and who attained age fifty before April first, nineteen hundred fifty-seven, or who attain such age on or after such date, beginning with the month when such local law, ordinance or resolution shall become effective, if such local retired employee is then fifty years of age or beginning with the month thereafter during which she attains age fifty. 3. Except as otherwise provided by or pursuant to subdivision five or subdivision six of this section, the monthly supplemental pension to be paid to a state retired teacher shall be twenty-five dollars plus the amount, if any, by which one-twelfth of his annual retirement allowance, computed without optional modification, is less than fifty dollars. In no event shall the monthly supplemental pension paid to a state retired teacher exceed an amount which, when added to an amount equal to one-twelfth of his annual retirement allowance, computed without optional modification, exceeds the sum of one hundred dollars. 4. For the purposes of this section, in determining the number of years of allowable and credited service, a major fraction of a year shall be counted as a full year. 5. Notwithstanding any other provision of this act but except as otherwise provided by or pursuant to subdivision six and subdivision seven of this section, any state retired teacher who

(a) attained age sixty-five before April first, nineteen hundred fifty-six, or who attains such age on or after such date and who is receiving or is entitled to receive a supplemental pension pursuant to this act on or after such date shall, beginning with the month of April, nineteen hundred fifty-six, if he is then sixty-five years of age or beginning with the month thereafter during which he attains age sixty-five, or

(b) is a female person who attained age sixty-two before April first, nineteen hundred fifty-seven, or who attains such age on or after such date and who is receiving or entitled to receive a supplemental pension pursuant to this act on or after such date shall, beginning with the month of April, nineteen hundred fifty-seven, if she is then sixty-two years of age or beginning with the month thereafter during which she attains age sixty-two, or

(c) is retired for disability, either before or after attaining age fifty, and who attained such age before April first, nineteen hundred fifty-seven, or who attains such age on or after such date and who is receiving or entitled to receive a supplemental pension pursuant to this act on or after such date shall, beginning with the month of April, nineteen hundred fifty-seven, if he is then fifty years of age or beginning with the month thereafter during which he attains age fifty, receive a monthly supplemental pension in an amount which when added to his monthly retirement allowance or pension, computed without optional modification, including any modification due to additional contributions as authorized by subdivision three of section five hundred sixteen of the education law shall be equal to one hundred eight dollars and fifty cents; provided, however, that this subdivision shall not become operative in the case of a local retired teacher unless and until a local law, ordinance or resolution authorizing such additional supplemental pension payments for such a person or persons shall have become effective. receive a monthly supplemental pension in an amount which when added to his monthly retirement allowance or pension, computed without optional modification, shall be equal to one hundred eight dollars and fifty cents; provided, however, that this subdivision shall not become operative in the case of a local retired teacher unless and until a local law, ordinance or resolution authorizing such additional supplemental pension payments for such a person or persons shall have become effective. 6. Notwithstanding any other provision of this act except as otherwise provided by or pursuant to subdivision seven of this section, (a) a state retired teacher, having retired prior to July first, nineteen hundred sixty-one, who is not receiving the primary benefit obtained under the federal old-age, survivors, and disability insurance system, shall receive, beginning with the month of September, nineteen hundred sixty-five, a monthly supplemental pension in an amount which when added to his monthly retirement allowance or pension, computed without optional modification, shall be equal to two hundred dollars and beginning with the month of September, nineteen hundred seventy, a monthly supplemental pension in an amount which, when added to his monthly retirement allowance or pension, computed without optional modification, shall be equal to two hundred twenty-five dollars, or (b) a state retired teacher, having retired prior to July first, nineteen hundred sixty-one, who is receiving the primary benefit obtained under the federal old-age, survivors, and disability insurance system, shall receive, beginning with the month of April, nineteen hundred sixty-five, a monthly supplemental pension in an amount which, when added to his monthly retirement allowance or pension, without optional modification, shall be equal to one hundred seventy-five dollars; provided, however, that this subdivision shall not become operative in the case of a local retired teacher unless and until a local law, ordinance or resolution authorizing such additional supplemental pension payments for such a person or persons shall have become effective, and further provided that nothing herein contained shall be construed to reduce any pension or retirement allowance, or supplemental pension being received by any retired teacher prior to April first, nineteen hundred sixty-five. As used in this subdivision the term "optional modification" includes modification due to additional contributions authorized by subdivision three of section five hundred sixteen of the education law. 7. For persons retiring after June thirtieth, nineteen hundred sixty and prior to the effective date of this chapter, and who are otherwise eligible for supplementation under provisions of this act, a retroactive payment for supplemental pensions shall be made, as if chapter one thousand forty of the laws of nineteen hundred sixty had not been enacted, covering the period between the date of retirement and the effective date of this chapter.