NMAC BTWN AN INST INSTRUCTOR TRAINING FLT; IN CESSNA 172; ON AN ILS SHORT FINAL CLOSING ON A PIPER SENECA JUST AHEAD FOR LNDG. THE C172 MADE GAR IN TAKING EVASIVE ACTION.

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WHILE ON THE ILS RWY 7L APCH INTO DAYTONA BEACH INTL ARPT (DAB); MY INSTRUCTOR (CFI/CFII) AND MYSELF (CFI) NEARLY HAD A MIDAIR COLLISION INTO THE BACK OF A PIPER PA34 SENECA THAT WAS LNDG ON RWY 7L. AT THE TIME I WAS UNDER AN INST TRAINING HOOD FLYING THE APCH WHILE MY INSTRUCTOR WAS LOOKING FOR TFC OUTSIDE THE AIRPLANE. WE BEGAN THE APCH BY OBTAINING AN IFR CLRNC AND STARTING THE APCH NORMALLY. I DECIDED TO FLY THE APCH AT APPROX 120-130 KIAS. THIS WAS FASTER THAN I NORMALLY SHOT THE ILS APCH AT. I NORMALLY FLEW AT 90 KIAS FOR THE ILS RWY 7L APCH. I DECIDED TO FLY THE APCH AT A FASTER SPD BECAUSE WE WERE GIVEN NO SPD RESTRS BY DAYTONA BEACH APCH CTL AND CTL TWR. WE STARTED THE APCH NORMALLY. I FLEW THE AIRPLANE ON THE ILS APCH THE ENTIRE TIME THROUGH GS INTERCEPTION DOWN THE GS APCHING THE DECISION HT OF 232 FT MSL. DSNDING THROUGH 500 FT EVERYTHING WAS NORMAL AND OUR AIRSPD WAS APPROX 120-130 KIAS. AT THIS TIME WE WERE TALKING TO THE DAYTONA BEACH CTL TWR AND HAD RECEIVED CLRNC TO LAND ON RWY 7L. WE HAD BEEN GIVEN NO TA'S OR SPD RESTRS. UPON REACHING APPROX 300 FT MSL MY INSTRUCTOR SAID TO IMMEDIATELY LOOK UP (AS I WAS UNDER AN INST TRAINING HOOD) AND I LOOKED UP TO SEE THE REAR END OF A PIPER PA34 SENECA APPROX 100-150 FT IN FRONT OF OUR AIRPLANE AND APPROX 50 FT BELOW OUR ALT. I IMMEDIATELY EXECUTED A GAR.I CALLED TO INFORM THE CTL TWR WE WERE GOING AROUND IN A VERY CONCERNED VOICE AND THEY TOLD US TO FLY L HAND TFC WITH SEEMINGLY NO CONCERN OR SURPRISE AT ALL. I DOUBT THE CTL TWR SAW THAT WE CAME VERY CLOSE TO THE PIPER SENECA. WE FLEW A NORMAL PATTERN AND MADE A NORMAL LNDG. THE CTL TWR NOR THE PIPER SENECA MADE ABSOLUTELY NO MENTION OF THE NEAR MIDAIR COLLISION. I WAS VERY CONCERNED THAT THE CTL TWR HAD NEVER WARNED US OF OUR PROX TO THE SENECA AND HAD NEVER GIVEN US A TA FOR THE SENECA. I FEEL IN THIS OCCURRENCE THAT THE DAYTONA BEACH CTL TWR FAILED OUTRIGHT TO WARN US AND SEPARATE OUR AIRPLANE FROM GETTING TOO CLOSE TO THE PIPER SENECA. THIS WAS A CLOSE CALL AND IF WE HAD CONTINUED ON THE APCH TO LAND ON THE RWY WE MAY HAVE COLLIDED WITH THE SENECA. MY INSTRUCTOR DID NOT TAKE THE FLT CTLS OR INITIATE THE GAR SO I FEEL I MAY HAVE BEEN MORE SCARED AND MORE CONCERNED THAN THE SIT ACTUALLY WARRANTED. I FEEL THAT THE CTL TWR DID NOT EXPECT OUR AIRPLANE TO BE IN THE POS THAT IT WAS; SO THEY MAY NOT HAVE EVEN SEEN OUR AIRPLANE GETTING SO CLOSE TO THE SENECA. I VIEW MY DECISION TO FLY THE ILS APCH AT A FASTER THAN NORMAL SPD AS A FACTOR IN THIS OCCURRENCE. WHILE WE COULD FLY THE APCH SAFELY AT THIS SPD; AND WHILE WE WERE GIVEN NO SPD RESTR FOR THE APCH; I THINK IT PUT OUR AIRPLANE IN A POS WHERE THE CTL TWR DID NOT EXPECT US TO BE. HAD WE NOTIFIED THE CTL TWR OF OUR ABOVE NORMAL APCH SPD; THEY MIGHT HAVE TAKEN GREATER CONCERN WITH OUR POS IN RELATION TO THE OTHER ACFT.