Question

Can i get a solution to the question step by step using excel or hand writing showing me how to get that "exact same value" which was given as a correct answer from the question please . Thank you for helping !

Problem #1: A bond issued on February 1, 2004 with face value of $25800 has semiannual coupons of 8%, and can be redeemed for par (face value) on February 1, 2025. 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 10%? (use actual actual for accrued interest) accrued interest and market price (in that order) separated with a comma Problem #1 : 594.52,20893.97 both answers correct to 2 decimals Correct Answer: 594.52, 21506.52

Answer 1

Face value (F) = redemption value (C) = $25800

Semiannual coupon rate (r) = 0.08/2 = 0.04

Semiannual yield rate (j) = 0.1/2 = 0.05

Number of compounding periods till maturity: 42-5 = 37

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)(25800)(0.04) = 594.52

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=37 and j = 0.05)

P(0) = 25800 + 25800 (0.04-0.05)(16.71) = 21488.49

Therefore the market price is:

21488.49(1.05^(106/184))-594.52 = 21506.52