Question

what should you pay for a semi annual bond that has a coupon rate of 7 percent, has a face value of $1000, matures 7 years and has a market rate return to 8 percent?

Answer 1

Solution:
	Amount willing to pay for the Bond is $947.18
Working Notes:
Notes:	Amount willing to pay for the Bond is Price of the bond , which is the present value of all cash flow during the life of bond . And will be computed as follows.
	Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond
	Coupon Rate = 7%
	Annual coupon = Face value of bond x Coupon Rate = 1,000 x 7% = $70
	Semi annual coupon = Annual coupon / 2 = $70/2=$35
	YTM= 8% p.a (annual)   The market rate of return for the bond is its YTM Yield to maturity
	Semi annual YTM= 8%/2 = 4%
	n= no.of coupon = No. Of years x no. Of coupon in a year = 7 x 2 =14
	Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond
	= $35 x Cumulative PVF @ 4% for 1 to 14th + PVF @ 4% for 14th period x 1,000
	= $35 x 10.56312293 + 1000 x 0.577475083
	947.1843856
	=$947.18

Cumulative PVF @ 4 % for 1 to 14th is calculated = (1 - (1/(1 + 0.04)^14) ) /0.04 = 10.56312293

PVF @ 4% for 14th period is calculated by = 1/(1+i)^n = 1/(1.04)^14 =0.577475083

Please feel free to ask if anything about above solution in comment section of the question.