Maddin

The reason for the difference of rate used is quite easy to figure out.

For FRA: you settle the FRA at the BEGINNING of the period and since

- interest is paid AT THE END of the period
- LIBOR is "forward-looking" rate (i.e., rate to be used for the coming period).

You need to use the current rate to know what (interest difference) you need pay AT THE END of the period then discount it back (to the beginning of the period) to calculate the pay out.

While SWAP: just regular swapping of interest to be paid at the end of the (last or each) period (which by convention is the beginning of the next period).
So to you calculate what interest you own, you need the rate at the beginning of last period since you are now at the end of last period. No discounting is required since you are paying it now.


Hope it makes sense