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Answer: Company receives $24,631
## Explanation In a Forward Rate Agreement (FRA), the company has agreed to **pay** a fixed rate of 5.0% and **receive** the floating rate (90-day LIBOR). Since the actual LIBOR rate (6.0%) is higher than the fixed rate (5.0%), the company will **receive** the difference. ### Calculation: - **Notional amount**: $10,000,000 - **Rate difference**: 6.0% - 5.0% = 1.0% - **Time period**: 90 days = 90/360 = 0.25 years - **Quarterly compounding**: All rates are expressed with quarterly compounding **Payment formula for FRA settled in advance**: \[ \text{Payment} = \frac{\text{Notional} \times (R_{\text{floating}} - R_{\text{fixed}}) \times \text{Time}}{1 + R_{\text{floating}} \times \text{Time}} \] \[ \text{Payment} = \frac{\$10,000,000 \times (0.06 - 0.05) \times 0.25}{1 + 0.06 \times 0.25} \] \[ \text{Payment} = \frac{\$10,000,000 \times 0.01 \times 0.25}{1 + 0.015} \] \[ \text{Payment} = \frac{\$25,000}{1.015} = \$24,630.54 \approx \$24,631 \] Since the company receives the payment (floating rate > fixed rate), the correct answer is **Company receives $24,631**.
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A company wants to borrow $10 million for 90 days starting in one year. To hedge the interest rate risk of the future borrowing, the company enters into a forward rate agreement (FRA) where the company will pay a fixed rate, R(k), of 5.0%. The FRA cash settles in one year; i.e., in advance (T=1.0) not in arrears (T=1.25). All rates are expressed with quarterly compounding. If the actual 90-day LIBOR observed one year forward turns out to be 6.0%, what is the cash flow payment/receipt by the company under the FRA?
A
Company pays $24,631
B
Company pays $25,000
C
Company receives $24,631
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