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23 January, 10:07

Rhiannon Corporation has bonds on the market with 18.5 years to maturity, a YTM of 6.50 percent, and a current price of $1,048. The bonds make semiannual payments. What must the coupon rate be on these bonds

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  1. 23 January, 12:14
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    6.94%.

    Explanation:

    The number of coupons payments given is semi annual, the annual will be

    = 18.5 years to maturity * 2

    = 37 payments.

    Annual Yield to Maturity = 6.50 % / 2

    = 3.25 %

    For coupon payments we use formula:

    Bond Price = (Par value / 1 + r^t) + C (1 - 1 / 1 + r^t) / r

    $1,048 = ($1,000 / 1.0325^37) + C (1 - 1 / 1.0325^37) / 0.0325

    $1,048 = $306.24 + C $21.35

    $21.35 * C = $1,048 - $306.24

    Coupon Payment C = $741.75 / $21.35

    C = $34.74

    C = $34.74 * 2 = $69.48

    coupon rate = $69.48 / $1,000

    Coupon rate = 6.94%.
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