Question

You purchase a bond with an clean price of $1016. The bond has a coupon rate of 5 percent, and there are 5 months to the next semiannual coupon date. What is the dirty price of the bond? Enter the answer with 2 decimals (e.g. 954.23).

Answer 1

Dirty Price of the Bond is simply the sum of Clean Price and Accrued Interest. Accrued Interest is the amount that has accumulated since last interest payment. In the above question, the interest is being paid semiannually & there are 5 months to next coupon date. That means, we have to calculate accrued interest on 1 month(6-5 months).

Let's see the calculation of Accrued Interest first:

Coupon Rate= 5% & Par value is taken to be $1000

Interest for one month shall be (5% of 1000)*1/12 ie. $4.17

Note: I have divided the annual interest by 12 since we have to calculate interest for one month only for calculating accrued interest.

Now we are given that Clean Price is $1016 and we have calculated accrued interest of $4.17

We can calculate Dirty Price by adding Clean Price to Accrued Interest.

Dirty Price = 1016 + 4.17

Dirty Price = $1020.17