Try this...
declare @Dayname varchar(25)
declare @Min_disburment_date datetime
set @Dayname = 'Saturday'
set @Min_disburment_date = '15-Aug-2013'
select @Dayname, @Min_disburment_date, DateName(weekday,@Min_disburment_date)
WHILE DateName(weekday,@Min_disburment_date) <> @Dayname
BEGIN
SET @Min_disburment_date = dateAdd(d,1,@Min_disburment_date)
END
select @Dayname, @Min_disburment_date, dateAdd(d,7,@Min_disburment_date), dateAdd(d,14,@Min_disburment_date)