RBAI will meet Ballymena Academy in the final of the Danske Bank Medallion Shield after Saturday's semi finals.
Inst recorded a 29-5 win over Sullivan Upper at Pirrie Park and Ballymena eliminated Down High 29-6 at Osborne Park to reach the final at Upper Malone on March 11.
Ballymena were flattered by their victory as the scoreline did not reflect the competitiveness of the tie
Coach Stephen Johnston said: "Credit to Down High who took the game to us as we had to weather a lot of pressure."
Indeed, Down had numerous opportunities to score tries but the final pass, time after time, let them down.
The Co Antrim side went 10 points up with Conor Barkley and Conor Gallagher triesl.
Just after the restart a pushover try goaled by Conor Agnew extended Ballymena's lead and further tries from out-half Angus Kernaghan and substitute winger Andrew Adams, one of which was goaled, completed Ballymena's scoring. Patrick Browne kicked Down's penalties.
Down coach Danny Carson said: "Maybe it was the big occasion and nerves but we should have scored a number of tries."
Inst had a four-try victory over Sullivan. James Hume kicked a penalty after 12 minutes and then added the points to a try from winger Sam Fryers to give them an eight-point interval lead.
The Holywood team came back with a Michael Houston try but Inst then scored tries by Callum Reid and Michael Lowry within five minutes.
Substitute Adam Gowdy crashed over just before the hour and Hume converted all three.