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A couple things. "Add-on interest" refers to the fact that LIBOR is not quoted at a discount where Treasury bills are, which is called "discount interest". (CFAI, Vol. VI, pp. 14,15)

Next, here is the CFA formula for valuing an FRA mid-contract to the long (ibid, pp. 37)


Vo = Notional Principal multiplied by --->

1 / [1 + (new short-term rate x days/360)] - [1 + (FRA rate x days/360)] / [1 + (new long-
term rate x days/360)]

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