Question

57. Three years ago, you bought an 8% coupon bond with a 9-year remaining maturity for $936. Today you sold the bond for $1,069. Given that the bond paid coupons semiannually, what was your effective annual rate of return on this investment?

Answer 1

Solution:
	Effective annual rate of return	12.99%
Working Notes:
Notes:	Effective annual rate of return for 3 years returns is calculated
	As the bond is paying coupon semi annually , its Ytm can be calculated by Excel or financial calculator
	No. of period = Period of investment x no. of coupon in a year = 3 x 2 =nper = N = 6
	Face value of bond = FV= $1069    amount received after selling at end of 3rd year
	Price of the bond = PV = -$936      Amount paid for Buying at beginning of 3 years
	Semi-Annual Coupon amount = PMT = coupon rate x face value /2= 8% x $1,000/2 =$40
	For calculation semi annual YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(6,40,-936,1069)
	6.295495828%
	Semi annual YTM 6.295495828%
	Effective Annual rate (EAR) = (1+r/m)^m -1
	m is the number of compounding periods per year = bond is semi annual means 2 times in a year = 2
	(r/m) is the interest rate per semi annual period = 6.295495828%
	Effective Annual rate (EAR) = (1+r/m)^m -1
	Effective Annual rate (EAR) = (1+ 6.295495828%)^2 -1
	Effective Annual rate (EAR) = 0.129873243
	Effective Annual rate (EAR) = 0.1299
	Effective Annual rate (EAR) = 12.99%
Please feel free to ask if anything about above solution in comment section of the question.