Forward Rate Agreement

[lmakombo]

An FRA trader entered into an FRA agreement in which he will pay 6%(assuming quarterly compounding) between 3 months and 6 months. The principal for the trade is $3 million. The 6 month LIBOR spot rate is 5.8%. If the trader had a gain of $2550 at the end of the period, The 3 month LIBOR rate would be?

A. 5.30%
B. 6.30%
C. 5.25%
D. 2.51%

The correct answer is A. how do we get there??????????????????

 

[ShaktiRathore]

Let x be the libor rate between the 3 months and 6 months [e^x*.25-(e)^.25*.06]*3000000=2550
[e^x*.25-(e)^.25*.06]=[2550/3000000]=.00085
(e)^x*.25=1.015113
(e)^x*.25=1.01596
.25x=.015836
x=6.334%
3 month libor as of today=(e)^.5*.058/(e)^.25*.06334=1.0294246/1.015963=1.01325=(e^3 month libor*.25)=>.25*3 month libor=.013163=>3 month libor=.05265=.0527~.053(rounding off to next higher place decimal)

thanks