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FRM Part I · FRM Exam Part I · Bond Yields and Return Calculations

A Treasury note has a 6% annual coupon paid semiannually and a face value of 100. The coupon period is 182 days and 40 days have elapsed since the last coupon. An investor pays a total (dirty) price of 101.80 per 100 face. Using actual/actual, what is the quoted (clean) price, to two decimals?

The clean price is 101.14. Accrued interest is the 3.00 semiannual coupon times 40/182, or 0.66. Quoted prices exclude accrued interest, so it is subtracted from the dirty price of 101.80. Adding it, or using the annual coupon in the accrual, gives the wrong result.

  1. A101.14Correct
  2. B102.46
  3. C98.80
  4. D100.48

Explanation

The semiannual coupon is 3.00. Accrued interest = 3 x 40/182 = 0.6593. The clean price = dirty price - accrued interest = 101.80 - 0.66 = 101.14. The 102.46 option adds the accrued interest instead of subtracting it. The 98.80 option subtracts a full coupon. The 100.48 option uses the annual coupon of 6 to compute accrued interest.

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