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Help with SOA 43

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  • Help with SOA 43

    A 10,000 par value bond with coupons at 8%, convertible semiannually, is being sold 3 years and 4 months before the bond matures. The purchase will yield 6% convertible semiannually to the buyer. The price at the most recent coupon date, immediately after the coupon payment, was 5640. Find the market price of the bond.

    Solution:

    Price = 5640*1.03^(1/3) - 400*(1.03^(1/3)-1)/(1.03-1)

    Can someone explain how this is derived? I thought that because the price of the most recent coupon date was 1/3 month before, the market price is just 5640 accumulated at 2 months, which is 1/3 of the 6-month period. I don't get the subtraction term. Thank you.
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