Optional settlement 4 consists of the right to elect in writing to have a retirement allowance paid him or her until his or her death and thereafter to have other benefits as are approved by the board, upon the advice of the actuary, continued throughout the life of and paid to the persons, having an insurable interest in his or her life, as he or she nominates by written designation duly executed and filed with the board at the time of his or her retirement. The designation shall not, in the opinion of the board and the actuary, place any additional burden upon the retirement system.