Any appointed full-time employee, who shall be a member of a city employees’ pension fund, including librarians and other employees of a public library, and full-time employees of a city recreation commission, of a city having an employees’ pension fund who shall have served two hundred forty months or more, whether or not consecutive, as an employee and shall have reached the age of sixty years, or who, while employed by such city, shall suffer permanent mental or physical disability so that the person is unable to discharge the person’s duties, shall be entitled to be retired. Upon retirement, the person shall be paid out of the pension fund of such city a monthly pension of not to exceed sixty percent of one-twelfth of the person’s highest three-year average annual earnings as provided for in the plan adopted by the governing body of the city. If any member shall have served two hundred forty months in such city employment but shall not have reached the age of sixty years, the person shall be entitled to retirement, but no pension shall be paid while the person lives until the person reaches the age of sixty years.