A member entitled to a retirement annuity may elect at the time of retirement to receive a reduced retirement annuity and provide with the actuarial value of the reduction, determined on an actuarial equivalent basis, a reversionary annuity for any person who is dependent upon the member at the time of retirement, as named in a written direction filed with the system as a part of the application for the retirement annuity, provided that the reversionary annuity is not less than $10 per month, nor more than the reduced retirement annuity to which the member is entitled. The condition of dependency must be established and proved to the satisfaction of the system before the election becomes effective.
     The reversionary annuity shall begin as of the first day of the month following the month in which the death of the annuitant occurs, provided, that the designated beneficiary is then living. If the designated beneficiary predeceases the annuitant, the reversionary annuity shall not be payable, and beginning the first of the month following notification of the designated beneficiary’s death, the System shall pay the annuitant the retirement annuity he or she would have received but for the reversionary annuity election.