§ 513. Optional allowances. 1. With the exception that no election of an optional benefit shall become effective in case a member dies within thirty days after the filing of an application for a retirement allowance, until the first payment on account of any benefit becomes normally due, any member, at the time of his retirement, may elect to receive his benefits in a retirement allowance payable throughout life or he may on retirement elect to receive the actuarial equivalent at that time of his retirement allowance in a lesser retirement allowance, payable throughout life with the provision that:

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Option 1. If he die before he has received in payments the present value of his retirement allowance as it was at the time of his retirement, the balance shall be paid to his legal representatives or to such person as he shall nominate by written designation duly acknowledged and filed with the retirement board.

Option 2. Upon his death, his retirement allowance shall be continued through the life of and paid to such person as he shall nominate by written designation duly acknowledged and filed with the retirement board at the time of his retirement.

Option 3. Upon his death, one-half of his retirement allowance shall be continued throughout the life of and paid to such person as he shall nominate by written designation duly acknowledged and filed with the retirement board at the time of his retirement.

Option 4. Some other benefit or benefits shall be paid either to the member or to such person or persons as he shall nominate, provided such other benefit or benefits, together with the lesser retirement allowance, shall be certified by the actuary to be of equivalent actuarial value to his retirement allowance and shall be approved by the retirement board.

2. If any retired member who has not elected an optional benefit, or who has elected a benefit under Option 4 providing for the payment at death of the amount, if any, by which his accumulated contributions at the time of his retirement exceed the aggregate amount of his annuity payments, dies within thirty days after the date his retirement becomes effective, notwithstanding any other provisions of this law to the contrary, benefits shall be paid in accordance with subdivision (b) or (c) of section five hundred twelve, except that the amount of his accumulated contributions payable under paragraph (1) of said subdivision (b) shall be reduced by any annuity payments received by him prior to his death and the benefit payable under paragraph (2) of said subdivision (b) shall be reduced by any pension payments received by him prior to his death. The amounts payable shall be paid to the beneficiary or beneficiaries entitled thereto as provided under section five hundred twelve, except that if the member has elected Option 4, as provided above, the beneficiary nominated under such Option 4 shall be substituted for any beneficiary previously nominated and all amounts payable shall be paid to the beneficiary nominated under such Option 4.

3. In the case of persons who last became members on or after July first, nineteen hundred seventy-three, the provisions of subdivision two of this section shall apply only to deaths occurring after the date on which said subdivision two becomes operative and prior to July first, nineteen hundred seventy-four.

4. a. The retirement board may adopt rules and regulations providing that a trustee of an inter vivos or testamentary trust shall be (1) eligible to be nominated to receive a lump sum benefit under option one and (2) eligible to be nominated to receive any benefit under option four which the retirement board shall deem appropriate.

b. Any proceeds received by a trustee under this section shall not be subject to the debts of the member or to transfer or estate taxes to any greater extent than if such proceeds were payable to the beneficiaries named in the trust and not to the estate of the member.

c. A payment made in good faith under this section to either a designated trustee of an inter vivos trust, a successor trustee of an inter vivos trust who provides a copy of his appointment or a trustee or successor trustee of a testamentary trust who provides a copy of the letters of trusteeship shall be a complete discharge to the system to the extent of the payment.

d. If no qualified trustee claims the proceeds within eighteen months after the death of the retired member, or if satisfactory evidence is furnished within such period showing that there is or will be no trustee to receive the proceeds, payment shall be made to the deceased retired member's estate.