Forward Rate Agreement Problem

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keep_running

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Company buys $ 10 million dollar 7 x 10 FRA at fixed rate 6.75%
3 month interest rates at initiation and expiration are 5.5% and 5.2%, respectively.
How much does the company pay at expiration of the forward contract?
I am completely new to the notation in this type of problem. Also I am not exactly sure how they got the answer as well.
Specifically, I am not sure why they would discount the original payment that is calculated (38,750) to a “present value”, (38,252). What is the reasoning for this?
Thanks!
 
A 7X10 FRA implies a rate that is locked beginning Seven months from now for a period of Three months - [On Jan 1st a 7X10 FRA implies a rate locked in from Aug 1st to Nov 1st. The FRA is settled on Aug 1st at the rate prevailing then]
The whole contract ends after Ten months. In this case, the FRA is initiated now where the rate locked is for borrowing money at 6.75% seven months from now for a period of three months (from the seventh to the tenth month). The 3 month rate right now is 5.5% and after seven months when the FRA expires it is 5.2%.
The P/L calculation is = $10m * [(5.2% - 6.75%)*(90/360)] = - $38,750. The answer is negative indicating a payment to be made since the borrower has locked the rate of interest because he expected rates to rise but it did not.
This payment will be made in the tenth month equalling $38,750. But, FRAs are generally settled in advance and thus the contract is settled in the Seven month rather than the Tenth month. So, they “Present Value” it at 5.2% which gives ($38,252).
And remember that 5.2% is used and not 5.5% since the FRA settlement is done in the Seventh month when it expires whereas it was initiated now.
Hope this helps!
 
Ok, so since the FRA is settled in the 7th month, the settlement between the two parties occurs in the 7 months, which is basically the value of the exchange (38,750) in the 7th month?
 
Correct.
38,750 is the value 10 months from inception, but the FRA is settled 7 months from inception.
 
Keep_running where did you see this question? As far as I know, concept of FRA is covered but calcualation is not included in CFA Level 1 curriculum. Fix me if I am wrong please.
 
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