Question

Suppose that a U.S. Treasury note maturing February10, 2009 is purchased with a settlement date of July 31, 2007. The coupon rate is 3% and the maturity value of the position is $1,000. The next coupon date is August 15, 2007. What is the full (dirty) price of this bond given the required yield is 4.0%? (Note that there 181 days in the coupon period and there are 15 days between the settlement date and the next coupon date.)

1000.72

992.72

$989.81

$971.99

Answer 1

Period	Discounting Factor [1/(1.02^period)]	Discounting Factor Annuity (Sum of discounting factor & all previous discounting factors)
1	0.980392157	0.980392157
2	0.961168781	1.941560938
3	0.942322335	2.883883273
4	0.923845426	3.807728699

Flat Price or Clean Price (i.e. Price as on February 10, 2007) = PV of All Coupons + PV of Maturity Value = [Coupon*Annuity Factor] + [Maturity Value*Discounting Factor] = [1000*1.5%*3.8077] + [1000*0.9238] = 57.1155 + 923.8 = $980.9155

Invoice Price or Dirty Price = Flat Price + Accrued Interest till Purchase Date = 980.9155 + [1000*1.5%*(181-15)/181] = 980.9155 + 13.7569 = $994.6724 which is equivalent to $992.72