Question

AT&T 10-year, $1,000 par value bond is selling at $1,158.91. Interest on this bond is paid semiannually.

If the annual yield to maturity is 14%, what is the annual coupon rate of the AT&T bond?

Answer 1

Step-by-step explanation:

Using YTM formula :

YTM = [PMT + {(FV-P) / n}] / [(FV+P)/2]

YTM = Yield to maturity = 14% = 0.14

PMT= Annual interest amount

FV = Face Value = $1000

P = Price =$1158.91

n = years to maturity = 10

0.14 = [PMT + {(1000 -1158.91) / 10}] / [(1000 +1158.91)/2]

0.14 = (PMT - 15.891) / 1079.455

PMT- 15.891 = 1079.455 * 0.14

PMT - 15.891 = 151.1237

PMT = 151.1237 -15.891

PMT = 135.23

So, Annual interest = $135.23

Annual interest rate = Annual interest / Face Value

= 135.23 / 1000

= 0.1352

=13.52%

Hence Annual Interest rate on the bond is 13.52%