Question

A bond issued on February 1, 2004 with face value of $32400 has semiannual coupons of 4%, and can be redeemed for par (face value) on February 1, 2022. What is the accrued interest and the market price (the “clean” price) of the bond on November 15, 2006, if the bond’s yield on that date is to be 7%? (use actual/actual for accrued interest).

Answer 1

Face value (F) = redemption value (C) = $32400

Semiannual coupon rate (r) = 0.04/2 = 0.02

Semiannual yield rate (j) = 0.07/2 = 0.035

Number of compounding periods till maturity: 36-5 = 31

Number of days since the last coupon = 106

Number of days in a coupon period = 184

Therefore t = 106/184

Therefore the accrued interest is:

tFr = (106/184)(32400)(0.02) = 373.30

The market price = (price plus accrued at time t) - accrued interest

Price plus accrued at time t = (P(0))((1+j)^t) - tFr

P(0) = F + F(r-j)(PV factor with n=31 and j = 0.035)

P(0) = 32400 + 32400 (0.02-0.035)(18.74) = 23294.17

Therefore the market price is:

23294.17(1.035^(106/184))-373.30 = 23387.12