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So with a 2 by 5 FRA, all it means is that the contract expires in 2 months time, BUT the UNDERLYING asset (i.e. the loan) will start in 2 months and ends in 5 months (both are from now).
In algebraic terms, a n by m FRA is the contract expires in n months time, but the underlying asset will start in n months and ends in m months with the duration of m-n months.
As for the difference between FRAs and IRSs, with the FRA you agree to pay a fixed rate, but for an IRS you either pay a fixed rate AND receive a float rate (or vice versa), on top of the settlement date differences.
does that make sense @eprak22?