20 million FRA payoff at expiration doubt!

CFA Level I Derivatives
#1

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,

#2

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.

#3

thanks for the explanation

#4

You’re welcome.