How accrued interest is included in the Full price?

Hi all,

I just didn’t understand how discounting a cash flow with the fraction of ( days between settlement date and next coupn payment date / days in coupon period) will give a FULL price that will include the accrued interest. I thought it would give a clean price.

For example, (referece : pg 500, CFAI Book intro to valuation of debt securities)

5 semiannual coupon remaining

8% annual discount rate

78 days between settlement date and the next coupon date

182 days in coupon period

we will have a price of $106.8192.

when if we calculate the bond price at the begining (without any thing mentioned above, this is regular valuation using n=1,2,3 and so on) then the price is $104.45

so now what i don’t understand here is how that $106.8192 included the Accured interest rate WITHOUT computing Days in Accrued interest period ( 110 days).

Any explanation would be great.