I assume you want this for a wider scope of data than you are using in your example.
Here is one way to do that (you may need to tweak this but the concept should be close).
if MInute({table.time})<16 then
dateadd("n",15-minute({table.time}),{table.time}) else
if Minute({table.time})<31 then
dateadd("n",30-minute({table.time}),{ACTIVITIES.STARTTIME}) else
if Minute({table.time})<46 then
dateadd("n",45-minute({table.time}),{table.time}) else
if Minute({table.time})<60 then
dateadd("n",60-minute({table.time}),{table.time})