Question

The yield to maturity of a $1000 bond with a 7% coupon rate, semiannual coupons, and two years to maturity is 7.6% APR, compounded semiannually. What must its price be?

Answer 1

Solution:
	Its price must be $989.06
	[The bond current price]
Working Notes:
	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= 7.6% p.a (annual)
	Semi annual YTM= 7.6%/2 = 3.8%
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= 2 x 2 = 4
	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 @ 3.8% for 1 to 4th + PVF @ 3.8% for 4th period x 1,000
	= 35 x 3.647069935 + 1000 x 0.861411342
	=$989.05878973
	=$989.06
Cumulative PVF @ 3.8 % for 1 to 4th is calculated = (1 - (1/(1 + 0.038)^4) ) /0.038 = 3.647069935
PVF @ 3.8% for 4th period is calculated by = 1/(1+i)^n = 1/(1.038)^4 =0.861411342
Please feel free to ask if anything about above solution in comment section of the question.