Question

Suppose that a bond is purchased between coupon periods. The days between the settlement date and the next coupon period are 80. There are 182 days in the coupon period. Suppose that the bond purchased has a coupon rate of 7% and there are 8 semiannual coupon payments remaining. The par value of the bond is $100. a. What is the full price for this bond if a 6.2% annual discount rate is used? b. What is the accrued interest for this bond? c. What is the clean price of the bond?

Answer 1

Clean price+accrued interest=Full price

Clean price for this bond

if a 6.2% annual discount rate is used

to discount the coupon & maturity proceed cash flow of the bond,

is the present value of the balance 8 semi-annual coupons + PV of the face value along with the 8th semi-annual coupon pmut.

Price=((semi-annual coupon amt.*(1-(1+s/a discount rate)^-n)/s/a disc.rt.)+(FV/(1+s/a disc.rt.)^n)=

ie.Price=((100*7%/2)*(1-1.031^-8)/0.031)+(100/1.031^8)=

102.80

b.Accrued interest for this bond

100*7%/365*102= ( ie. 182-80=102 days of int. to seller)

1.96

so, full price= 102.80+1.96=

104.76

so, the answers are:

a.Full price= 104.76

b.Accrued interest= 1.96

c.Clean price=102.80