20 million FRA payoff at expiration doubt!

[archived_user]

Dear Forum,
I have a doubt suppose this situation I enter in a long FRA with a contract rate of 5% and a notional of 20 million USD, at the expiration the 180 day libor is 5,75% and the agreement expires in 60 days. the answer is
a) I receive 75000 usd
B) I receive 72932
C) A and B are both Wrong, If it is the case I would apreciate if you could explain the right answer
Thanks for the advice in advance,

 

[archived_user]

You’re long, so you pay fixed, receive floating.
The payoff is (5.75% − 5%) × $20,000,000 = $150,000, 240 days after inception (= 60 days + 180 days); the payoff at expiration is $150,000 / [1 + (5.75% × 180/360)] = $145,808.
There you go.

 

[archived_user]

thanks for the explanation

 

[archived_user]

You’re welcome.