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FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage

A Treasury note with a 4% coupon paid semiannually has its last coupon on January 15 and its next on July 15 of a non-leap year, a period of 181 actual days. It settles on April 15, which is 90 actual days after the last coupon. Using Actual/Actual, what is the accrued interest per 100 of face value (rounded to four decimals)?

Accrued interest is 0.9945 per 100. Actual/Actual measures the fraction of the actual coupon period that has elapsed, 90 of 181 days. Multiplying that fraction by the 2.00 semiannual coupon gives 0.9945.

  1. A1.0000
  2. B0.9863
  3. C0.9945Correct
  4. D1.9890

Explanation

The semiannual coupon is 2.00. Accrued = 2.00 × 90/181 = 0.9945. The 1.0000 option applies a 30/360 style fraction of 90/180. The 0.9863 option uses 4 × 90/365, which ignores the actual coupon period. The 1.9890 option uses the full annual coupon.

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