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22 May, 11:35

a 20000 par value bond matures on january 1, 2020. The bond pays coupons at the annual rate of 7%, payable semiannually. The nomial annual yield to maturity is 10% compounded semiannually. Find the price of the bond on August 25, 2005.

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  1. 22 May, 15:15
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    The answer is $15,680.66.

    Explanation:

    Semiannual coupon payment is 20,000 x 7% / 2 = 700

    * Present value of the bond as at 1st Jan 2006 is equal to:

    + Coupon payment at the time + Present value of 28 coupon payments in the next 14 years + Present value of face value repayment at the end of 14 years (14 x2 = 28 discounting periods) = 700 + (700/5%) x [1 - 1.05^ (-28) ] + 20,000/1.05^28 = $16,230.562

    * We discount the present value of the bond as at 1st January 2006 to August 25 2005 to find the price of the bond (from Aug 25 to 31st December there are 128 days, divided by 182.5 days for one period).

    16,230.562 / (1 + 5% x 128/182.5) = $15,680.66.

    So the answer is $15,680.66.
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