Explanation

FRA Settlement Calculation

Given:

• Notional amount: $10,000,000
• Fixed rate (Rk): 5.0% (paid by company)
• Actual floating rate: 6.0% (received by company)
• Time period: 90 days = 90/360 = 0.25 years
• Quarterly compounding
• Settlement in advance (T=1.0)

Step 1: Calculate the interest rate differential The company pays fixed (5.0%) and receives floating (6.0%), so the net position is: 6.0% - 5.0% = 1.0% advantage to the company

Step 2: Calculate the settlement amount For settlement in advance, we use the formula:

$\text{Settlement} = \frac{\text{Notional} \times (L - Rk) \times \frac{\text{Days}}{360}}{1 + L \times \frac{\text{Days}}{360}}$

Where:

• L = 6.0% = 0.06
• Rk = 5.0% = 0.05
• Days/360 = 90/360 = 0.25

$\text{Settlement} = \frac{10,000,000 \times (0.06 - 0.05) \times 0.25}{1 + 0.06 \times 0.25}$ $\text{Settlement} = \frac{10,000,000 \times 0.01 \times 0.25}{1 + 0.015}$ $\text{Settlement} = \frac{25,000}{1.015}$ \text{Settlement} = 24,630.54 \approx \`$24`,631

Step 3: Determine payment direction Since the company receives the higher floating rate (6.0%) and pays the lower fixed rate (5.0%), the company receives the settlement amount.

Therefore, the company receives $24,631 (Option C).

This payment compensates the company for the fact that they could have borrowed at a lower rate in the market, but are locked into paying 5.0% fixed.