Question

a) $200,000 U.S. Treasury 7 7/8% bond maturing in 2002 purchased and then settled on October 23, 1992, at a dollar price of 105-20 (this is the clean price) with a yield to maturity of 7.083% with the bond originally being issued at 11/15/1977. Face value per unit is $1,000.

i) Calculate the clean price of the bond issue

ii) Calculate the accrued interest of the bond issue

iii) Calculate the full price of the bond issue

b) $200,000 U.S. Treasury 7 7/8% bond maturing in 2002 purchased and then settled on October 23, 1992, at a dollar price (clean price) with a yield to maturity of 7.083% with the bond originally being issued at 11/15/1977.

Calculate the full price (per unit of the bond).

Note: On a per unit basis, the answers to(a)and(b)should be the same.Anydifferencemustbe due to rounding error only.

Answer 1

a)

i) Clean Price = 105-20 = 105.625% of Face Value

Clean Price = 1000*105.625%

Clean Price = 1056.25

ii) Accrued interest = Coupon payment for the period of last coupon payment to October 23, 1992.

The U.S. Treasury bond is semiannual coupon bond. Last coupon date is May 15, 1992.

Using 30/360 day count convention, Coupon payment period = 158 days , Coupon Payment semiannual = 39.375

Accrued Interest = (158/180)*39.375 = 34.562

Accrued Interest = 34.562

iii) Full Price? = Clean Price + Accrued InterestFull Price

Full Price = 1056.25 + 34.56

Full Price = $1090.81

b)

C= Coupon , r = yield , t= time to maturity = , F = face value

2t = 21,

Bond Price = Clean Price = $1057.98

Clean bond price means bond price without accrued interest from last coupon payment.

Dirty price = Clean Price + Accrued Interest

Accrued interest = Coupon payment for the period of last coupon payment to October 23, 1992.

The U.S. Treasury bond is semiannual coupon bond. Last coupon date is May 15, 1992.

Using 30/360 day count convention, Coupon payment period = 158 days , Coupon Payment semiannual = 39.375

Accrued Interest = (158/180)*39.375 = 34.562

Accrued Interest = 34.562

Dirty price = 1057.980 + 34.562

Dirty Price=Full Price = 1092.542