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29 June, 08:32

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?

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  1. 29 June, 08:47
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    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%
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