
Answer-first summary for fast verification
Answer: -£8,834.
## Explanation To value the FRA, we need to calculate the present value of the difference between the fixed rate and the current forward rate. **Given:** - Notional amount: £3,000,000 - Original fixed rate: 3.1% - Current forward rate (3 × 9 FRA): 2.7% - 9-month MRR: 2.5% - Time period: 180 days (6 months) **Step 1: Calculate the interest rate differential** \[ \text{Rate differential} = 3.1\% - 2.7\% = 0.4\% = 0.004 \] **Step 2: Calculate the interest amount** \[ \text{Interest} = £3,000,000 \times 0.004 \times \frac{180}{360} = £3,000,000 \times 0.004 \times 0.5 = £6,000 \] **Step 3: Discount to present value using 9-month MRR** \[ \text{PV} = \frac{£6,000}{1 + 0.025 \times \frac{270}{360}} = \frac{£6,000}{1 + 0.025 \times 0.75} = \frac{£6,000}{1.01875} = £5,889.57 \] Since the company is long the FRA and rates have decreased (from 3.1% to 2.7%), the value should be negative. Therefore, the value is approximately **-£5,890**. **Note:** The calculation shows -£5,890, which matches option B, not A. However, based on standard FRA valuation methodology, the correct answer should be **B** (-£5,890).
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Three months ago, a company entered into a long 6 × 12 forward rate agreement (FRA) for £3 million at a fixed rate of 3.1%. If today the quoted rate on a new 3 × 9 FRA is 2.7% and the 9-month MRR is 2.5%, the value of the original FRA to the company is closest to:
A
-£8,834.
B
-£5,890.
C
£5,890.