A bank sells a “three against six” $3,000,000 FRA for a three-month period beginning three months from today and ending six months from today. The purpose of the FRA is to cover the interest rate risk caused by the maturity mismatch from having made a three-month Eurodollar loan and having accepted a six-month Eurodollar deposit. The agreement rate with the buyer is 5.55 percent. There are actually 92 days in the three-month FRA period. Assume that three months from today the settlement rate is 6.15 percent. Determine how much the FRA is worth and who pays who—the buyer pays the seller, or the seller pays the buyer.

Note: Round your intermediate calculations to 6 decimal places. Round your answer to 2 decimal places. Assume 360 days in a year.  Answer like this (buyer pays eller or seller pays buyer), the absolute value of the FRA is ?

To solve this problem, let's break it down step by step:

1. **Given Data:**
   - Notional principal: $3,000,000
   - FRA period: 92 days (three months starting three months from today and ending six months from today)
   - Agreement (fixed) rate: 5.55% (0.0555)
   - Settlement rate (three months from today): 6.15% (0.0615)
   - Year convention: 360 days in a year

2. **Formula for the value of the FRA** (which is essentially the settlement payment):
   \[
   \text{Settlement amount} = \frac{\text{Notional Principal} \times (\text{Settlement Rate} - \text{Agreement Rate}) \times \frac{t}{360}}{1 + \text{Settlement Rate} \times \frac{t}{360}}
   \]
   Where:
   - $ \text{Notional Principal} = 3,000,000 $
   - $ \text{Settlement Rate} = 6.15\% = 0.0615 $
   - $ \text{Agreement Rate} = 5.55\% = 0.0555 $
   - $ t = 92 $ days (the number of days in the FRA period)

Let's calculate the value of the FRA.The absolute value of the FRA is $4,528.82.

Since the settlement rate (6.15%) is higher than the agreement rate (5.55%), the seller pays the buyer.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How is an FRA different from a standard interest rate swap?
2. What is the significance of using a 360-day year in financial calculations?
3. How would the FRA value change if the settlement rate were lower than the agreement rate?
4. Can FRAs be used for other currencies besides the Eurodollar?
5. What is the impact of a longer FRA period on its value?

**Tip:** Always double-check whether the interest rates are annualized, and adjust for the actual days in the period when performing FRA calculations.

A bank sells a “three against six” $3,000,000 FRA for a three-month period beginning three months from today and ending six months from today. The purpose of the FRA is to cover the interest rate risk caused by the maturity mismatch from having made a three-month Eurodollar loan and having accepted a six-month Eurodollar deposit. The agreement rate with the buyer is 5.55 percent. There are actually 92 days in the three-month FRA period. Assume that three months from today the settlement rate is 6.15 percent. Determine how much the FRA is worth and who pays who—the buyer pays the seller, or the seller pays the buyer.

Determine the value of a $3,000,000 FRA with a 5.55% agreement rate over a three-month period, comparing it to a settlement rate of 6.15%. Learn step-by-step calculations using interest rate derivative formulas to cover interest rate risks and who pays whom—the buyer or seller.

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