A $10,000 bond pays semi-annual coupons at j₂ = 7% every March 2 and September 2.The bond is redeemable at par and is purchased between coupon dates on May 15,2010 to yield j₂ = 6.5%.At the time of purchase there are 10 coupons remaining to be paid,plus the redemption value.What is the full (or dirty)price of the bond on May 15,2010?

Question

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The full (or dirty) price of a bond includes the accrued interest since the last coupon payment. Since the bond pays semi-annual coupons at a 7% annual rate, each coupon is $350 ($10,000 * 7% / 2). The bond is purchased on May 15, 2010, which is after the March 2 coupon payment, so there is accrued interest for 2 months and 13 days (March has 31 days). The bond yields 6.5% annually, so the present value of the remaining coupons and the redemption value must be calculated at this yield. The dirty price is the sum of this present value and the accrued interest. Given the options, the correct calculation aligns with choice B, $10,342.74, which accounts for both the present value of future cash flows discounted at the yield rate and the accrued interest up to the purchase date.

A $10,000 Bond Pays Semi-Annual Coupons at J2 = 7

A $10,000 Bond Pays Semi-Annual Coupons at J₂ = 7