Company M approaches its bank for a loan of $$1$m$.$ The bank quoted M $9\%$

fixed interest rate or Libor $+2\%.$ M$,$ based on its market analysis, expects that Libor

rate will go down in future, and, hence, opted for floating interest rate.

Another company N negotiated the same amount of loan from its bank, and the

bank quoted N a $12\%$ fixed interest rate or Libor $+3\%.$ Company N thought that

Libor might go up$,$ so it went for fixed interest rate.

Later both the parties changed their views on the expected interest rates in future

and wished to swap their interest rate through an intermediary. Calculate their

effective interest rate after swap. Assume intermediary commission as $1\%.$