A $10,000 bond pays semi-annual coupons at j₂ = 10% every January 5 and July 5.It is purchased on February 5,2010 to yield j₂ = 11%.The full (or dirty)price of the bond on February 5,2010 is $9578.38.Using the method that is most commonly used in practice,what would be the price of the bond on the coupon date,January 5,2010?

Question

Quizplus · Accepted Answer

To determine the price of the bond on January 5, 2010, we need to calculate the accrued interest from the last coupon payment on July 5, 2009. We can do this by using the following formula:
Accrued interest = Coupon payment x (Days from last coupon payment to settlement date / Days in coupon period)
The coupon payment is $10,000 x 10% / 2 = $500
The days from last coupon payment to settlement date is 214 days (from July 5, 2009 to February 5, 2010)
The days in the coupon period is 182 days (from July 5, 2009 to January 5, 2010)
Therefore, the accrued interest is $500 x (214 days / 182 days) = $587.91
To find the price of the bond on January 5, 2010, we need to subtract the accrued interest from the full price on February 5, 2010:
Price on January 5, 2010 = $9578.38 - $587.91 = $9490.47
The closest choice is B, which is $9490.95.

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

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