Question

A 10​-year bond pays interest of $27.70 semiannually, has a face value of $1,000​, and is selling for $749.84. What are its annual coupon rate and yield to​ maturity?

Answer 1

Solution:
	Annual coupon rate	5.54%
	Yield to maturity	9.46%
Working Notes:
	Semi-annual coupon = $27.70
	So annual coupon = Semi annual coupon x 2
	Annual coupon = $27.7 x 2 = $55.40
	Annual coupon rate = r%
	Annual coupon = par value of bond x annual coupon rate
	$55.40 = $1,000 x annual coupon rate
	Annual coupon rate = 55.40/1,000
	Annual coupon rate = 0.0554
	Annual coupon rate = 5.54 %
Now YTM
	As the bond is paying coupon semi annually , its Ytm can be calculated by Excel or financial calculator
	First we get the semi annual YTM
	No. of period = years to maturity x no. of coupon in a year = 10 x 2 =nper = N = 20
	Face value of bond = FV= $1,000
	Price of the bond = PV = $749.84 = -$749.84
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 5.54% x $1,000 /2=$27.7
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(20,27.7,-749.84,1000)
	=4.73198538%
	The YTM calculated is semi annual
	YTM (annual) = Semi annual YTM x 2
	YTM (annual) = 4.73198538% x 2
	YTM (annual)= 9.463970759 %
	YTM (annual) = 9.46%
Please feel free to ask if anything about above solution in comment section of the question.