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FRM Part I · FRM Exam Part I · Properties of Interest Rates

A company enters a 12x18 FRA as the fixed-rate payer (long position) on a notional of USD 10 million at an FRA rate of 4.00%. At the start of the FRA period (month 12), the 6-month reference rate is 4.80% (simple, actual accrual of 0.5 year). The FRA settles at month 12, with the payoff discounted at the reference rate. What is the settlement amount received by the company?

The company receives USD 39,062.50. The reference rate exceeds the FRA rate by 0.80%, giving 40,000 of interest over half a year, and since settlement occurs at the start of the period this is discounted by 1.024.

  1. AUSD 39,062.50Correct
  2. BUSD 40,000.00
  3. CUSD 80,000.00
  4. DUSD 40,960.00

Explanation

The undiscounted interest difference is 10,000,000*(0.048-0.040)*0.5 = 40,000, payable at month 18. Settling at month 12 requires discounting by 1+0.048*0.5 = 1.024, giving 39,062.50. The USD 40,000 option omits discounting, and USD 40,960 multiplies by 1.024 instead of dividing.

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