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11 May, 19:02

Union Local School District has bonds outstanding with a coupon rate of 3.1 percent paid semiannually and 22 years to maturity. The yield to maturity on these bonds is 3.4 percent and the bonds have a par value of $10,000.

What is the price of the bonds?

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  1. 11 May, 22:54
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    The price of the bond is $9,537.91

    Explanation:

    Coupon payment = $10,000 x 3.1 = $310 / 2 = $155

    Number of period = n = 22 x 2 = 44 semiannual periods

    Face Value = $10,000

    Yield to maturity = 3.4% yearly = 3.4% / 2 = 1.7% semiannually

    Price of bond is the present value of future cash flows, to calculate Price of the bond use following formula:

    Price of the Bond = C x [ (1 - (1 + r) ^-n) / r ] + [ F / (1 + r) ^n ]

    Price of the Bond = $155 x [ (1 - (1 + 1.7%) ^-44) / 1.7% ] + [ $10,000 / (1 + 1.7%) ^44 ]

    Price of the Bond = $155 x [ (1 - (1.017) ^-44) / 0.017 ] + [ $10,000 / (1.017) ^44 ]

    Price of the Bond = $4,774.94 + $4,762.97

    Price of the Bond = $9,537.91
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