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FRM Part I · FRM Exam Part I · Interest Rate Futures

A U.S. Treasury bond with a 6% annual coupon (paid semiannually) last paid a coupon 61 days ago. The next coupon is paid in 122 days, so the coupon period is 183 days. The face value is $100. Using the actual/actual day count convention, what is the accrued interest per $100 face value?

Accrued interest is $1.00 per $100 face value. Under actual/actual the semiannual coupon of $3 is multiplied by the fraction of the coupon period elapsed, 61 of 183 days, which is one third. Using the days remaining instead would wrongly give $2.00.

  1. A$0.9998
  2. B$1.0000Correct
  3. C$1.0167
  4. D$2.0000

Explanation

The semiannual coupon is 3. Accrued interest = 3 x 61/183 = 1.0000, since 61/183 = 1/3. The $2.0000 option uses the 122 days remaining instead of the 61 elapsed. The $0.9998 and $1.0167 options come from using 30/360 style approximations that do not apply here.

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