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14 October, 22:39

Travel has 7 percent, semiannual, coupon bonds outstanding with a current market price of $1,020.46, a par value of $1,000, and a yield to maturity of 6.72 percent. How many years is it until these bonds mature

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  1. 14 October, 22:48
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    Answer: 9.685 years (approximately 9.7years)

    the bond would take 9.685 years to mature

    Explanation:

    Using yield to maturity formula

    YTM = C + (fv - pv) / n : (fv + pv) / 2

    C = coupon rate = 7% of par value

    = (7/100) * 1000

    = $70

    Fv = face value (par value) = $1,000

    Pv = price = $1,020.46

    YTM = yield to maturity = 0.0672

    n = number of years to maturity ... ?

    Using the above formula;

    0.0672 = 70 + (1000-1020.46) / n : (1000+1020.46) / 2

    0.0672 = 70 + (-20.46) / n : (2020.46) / 2

    0.0672 = 70 + (-20.46) / n : 1010.23

    70 - (20.46) / n = 0.0672 * 1010.23

    70 - (20.46) / n = 67.887456

    -20.46 / n = 67.887456 - 70

    -20.46 / n = - 2.112544 (Cross multiply

    -20.46 = - 2.112544n

    Divide both sides by - 2.112544

    n = 9.6850

    The number of years for the bond to mature is 9.685 years (approximately 9.7years)
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