You are considering buying a bond issued by General Motors with exactly 5.5 year

Question

You are considering buying a bond issued by General Motors with exactly 5.5 years remaining to maturity that just paid a coupon yesterday. It rained on your paper this morning so you do not know what the coupon rate is. However you are able to see that the quoted price is listed as $105-20 and the annualized yield is 7%, with semi-annual compounding. If the coupon is paid semi-annually, what is the quoted annualized coupon rate? Show your work

There are 2 answers on Chegg. Which one is correct? Please provide answer in Essay Format of possible

Explanation / Answer

Calculation of Coupon rate :

Formula :

YTM = 2*(C + (F-P)/n) / ((F+P)/2)

YTM = Yield to maturity = 7% = 0.07

F= Face Value = $100

P = Price = $105.20

C= Semiannual Coupon payment = F * Annualized coupon rate /2

n = number of semiannual = 5.5 years * 2 = 11

Hence ,

0.07 = 2*(C + (100-105.20)/11) / ((100+105.20)/2)

0.07 = 2*(C -0.4727273) / 102.6

0.07*102.60 / 2 = (C -0.4727273)

3.591 = C -0.4727273

C = 4.0637

Hence ,

F * Annualized coupon rate /2 = 4.0637

100 * Annualized coupon rate = 4.0637*2

100 * Annualized coupon rate = 8.1274

Annualized coupon rate = 8.1274/100

Annualized coupon rate = 8.13%

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