While every effort shall be made both by members and supervisory, personnel to keep the accumulation of time-off days at a minimum, in the event of the death of a member of the Department prior to retirement there shall be paid to his or her personal representative an amount equal to his or her daily rate of pay times the number of days of his or her accumulated time-off days; provided, however, that in no event shall payment be made for more than 15 time-off days. In computing time-off days, hours owed shall be converted into days at the rate of eight hours per day. Fractions of days in excess of 1/2 day shall be treated as a full day. Fractions of days less than 1/2 day shall be disregarded.