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Answer: Paid USD 43,875
## Explanation For the payment on July 31, 2022, we need to use the SOFR rate from July 1, 2022, which is 1.52%. **Calculation:** - Notional amount: USD 7,500,000 - Fixed rate received: 2.3% (annual) - Floating rate paid: SOFR + 1.95% = 1.52% + 1.95% = 3.47% (annual) - Net rate: Fixed rate - Floating rate = 2.3% - 3.47% = -1.17% (annual) - Since payments are made every 6 months, we divide by 2: -1.17% / 2 = -0.585% - Net amount: 7,500,000 × (-0.585%) = -43,875 The negative sign indicates the bank **paid** USD 43,875. **Why other options are incorrect:** - **B**: Result when rates aren't divided by 2 for semi-annual payment: 7,500,000 × (-1.17%) = -87,750 - **C**: Uses wrong SOFR rate (July 1, 2020): 7,500,000 × (2.3% - (0.11% + 1.95%))/2 = 9,000 - **D**: Ignores the 1.95% premium: 7,500,000 × (2.3% - 1.52%)/2 = 29,250
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A trader on the interest rate desk of a large bank entered into a customized 2-year interest rate swap contract on July 31, 2020, on a notional amount of USD 7.5 million. According to the terms of the swap, the bank received an annual fixed rate of 2.3% and paid an annual rate of SOFR as of the first day of the month of payment plus 1.95%. Payments were made every 6 months. The table below displays the relevant SOFR rates over the 2-year period:
| Date | 6-month SOFR |
|---|---|
| 1-Jul-20 | 0.11% |
| 1-Jan-21 | 0.10% |
| 1-Jul-21 | 0.05% |
| 1-Jan-22 | 0.05% |
| 1-Jul-22 | 1.52% |
Assuming no default, which of the following was the best estimate to the net amount that the bank paid or received on July 31, 2022?
A
Paid USD 43,875
B
Paid USD 87,750
C
Received USD 9,000
D
Received USD 29,250