A twenty year bond with a $1000 face value was issued with a yield to maturity of 4.5% and pays coupons semi-annually.After ten years,the yield to maturity is still 4.5% and the clean price of the bond is $960.09.After three more months go by,what would you expect the dirty price to be?

Question

Quizplus · Accepted Answer

Since the yield to maturity remains the same after ten years, we can assume that the bond is still trading at its par value of $1000. Therefore, the semi-annual coupon payments must be equal to the semi-annual yield of 2.25% multiplied by the face value of $1000, which gives us $22.50.

After ten years, there would be 20 - 10 = 10*2 = 20 semi-annual coupon payments left. Using the formula for the present value of a bond with semi-annual coupon payments, we can calculate the dirty price of the bond after ten years:

Dirty price = (20 * $22.50 / (1 + 2.25%)^20) + ($1000 / (1 + 2.25%)^20)
Dirty price = $466.59 + $532.50
Dirty price = $999.09

After three more months, one more coupon payment of $22.50 will be made. Therefore, the dirty price of the bond will be:

Dirty price = $999.09 + ($22.50 / (1 + 2.25%)^1)
Dirty price = $999.09 + $0.99
Dirty price = $1000.08
          
Therefore, the closest option to the expected dirty price is option B) $970.09.

A Twenty Year Bond with a $1000 Face Value Was