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Absolusia, an emerging economy

Absolusia, an emerging economy
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Absolusia, an emerging economy, has just made an issue of coupon-paying bonds, each with 3 years to maturity, and a face value of $1,000,000.Each bond has a coupon rate of 4% per annum, payable half-yearly.

The bonds have a yield of j2 = 6%, that is 6 per cent per annum, compounded half-yearly.

    (a) Calculate the current price of each $1,000,000 bond, correct to the nearer cent.
    (b) Calculate the duration of each bond. (Show 4 places of decimals).
    (c) Calculate the convexity of each bond. (Show 4 places of decimals).
    (d) You have just heard that, immediately after issue, the yield on the bond has increased from 6% per annum, compounded half-yearly, to 6.2% per annum, also compoundedhalf-yearly.

Using the formula (and/or the method) applied in (a) above, calculate the new bond price and the resultant price change, assuming that there are still 3 years until the bond's maturity.

    (e) Before the increase in yield in part (d) above took place, calculate the value of the bond at the duration date, as calculated in (b) above.

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