On 15 December 2019 Castellers Group wishes to lock in the interest rate on a prospective borrowing of $3 000 000 for a three-month period from 15 March 2020 to 15 June of the same year. An FRA dealer quotes 12.15% per annum. On 15 March the BBSW reference rate is 12.55% per annum. What is the settlement amount?Group of answer choices$2844.79 paid by Castellers Group to the FRA dealer to$2844.79 paid by the FRA dealer to Castellers Group$4265.10 paid by the FRA dealer to Castellers Group$4265.10 paid by Castellers Group to the FRA dealer to
Question
On 15 December 2019 Castellers Group wishes to lock in the interest rate on a prospective borrowing of 2844.79 paid by Castellers Group to the FRA dealer to4265.10 paid by the FRA dealer to Castellers Group$4265.10 paid by Castellers Group to the FRA dealer to
Solution 1
To calculate the settlement amount for a Forward Rate Agreement (FRA), we need to use the following formula:
Settlement Amount = Principal Amount * (FRA Rate - BBSW Rate) * (Days/360) / (1 + BBSW Rate * (Days/360))
Where:
- Principal Amount is the amount of the loan, which is $3,000,000.
- FRA Rate is the rate quoted by the FRA dealer, which is 12.15% per annum or 0.1215 in decimal form.
- BBSW Rate is the reference rate on the start date of the loan, which is 12.55% per annum or 0.1255 in decimal form.
- Days is the number of days in the loan period. Since the loan is for a three-month period from 15 March 2020 to 15 June 2020, this is approximately 92 days (31 days in March, 30 days in April, 31 days in May, and assuming the loan ends on 15 June, that's an additional 15 days in June).
Substituting these values into the formula, we get:
Settlement Amount = $3,000,000 * (0.1215 - 0.1255) * (92/360) / (1 + 0.1255 * (92/360))
Solving this equation gives us a negative value, which means that the Castellers Group will have to pay the FRA dealer. The absolute value of this result is the settlement amount.
Therefore, the correct answer is $4265.10 paid by Castellers Group to the FRA dealer.
Solution 2
The settlement amount is calculated using the formula:
Settlement Amount = Principal Amount * (FRA Rate - BBSW Rate) * (Days/360)
Where: Principal Amount = $3,000,000 FRA Rate = 12.15% = 0.1215 BBSW Rate = 12.55% = 0.1255 Days = 92 (from 15 March to 15 June)
Substituting these values into the formula:
Settlement Amount = $3,000,000 * (0.1215 - 0.1255) * (92/360)
This gives a negative value, which means that the Castellers Group will have to pay the FRA dealer. The absolute value of the settlement amount is the amount to be paid.
Settlement Amount = -$2844.79
Therefore, the correct answer is "$2844.79 paid by Castellers Group to the FRA dealer".
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