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

A US Treasury note pays a 4% annual coupon semiannually on face value 100, using actual/actual. The previous coupon date was March 1 and the next is September 1 (184 days apart). The trade settles on June 15. What is the accrued interest per 100 face value, to four decimals?

Accrued interest is 1.1522 per 100. Treasuries use actual/actual, so 106 actual days have elapsed in a 184-day coupon period. Multiplying the 2.00 semiannual coupon by 106/184 gives 1.1522. Applying 30/360 or a 180-day denominator produces different, incorrect figures.

  1. A1.0000
  2. B1.1522Correct
  3. C1.1556
  4. D1.1778

Explanation

Actual days from March 1 to June 15 = 30 (rest of March) + 30 + 31 + 15 = 106... check: March 1 to March 31 is 30 days, plus 30 in April, 31 in May, 15 in June gives 106 days wait to June 15 inclusive of the date arithmetic gives 106. Accrued = 2 × 106/184 = 1.1522. Using 30/360 gives 104 days and 1.1556, which is not the actual/actual convention; 1.1778 divides 106 by 180.

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