# Is this linear interpolation for clean bond price an approximation?

Consider the attached discussion from Berk and Demarzo's Corporate Finance.

I am confused about the calculation of a bond's "clean price". It seems that the procedure described above seems to tacitly "linearly discount" the accrued interest, rather than discounting cash flows with an appropriate factor. Put differently, why does the given graph suggest that Dirty Price grows linearly in between coupon payments, rather than according to some $$(1+r)^t$$ factor as would be expected based on (rigorous) discounting?

• The clean price is a convention which provides the buyer and seller a "common language" when they bargain with each other. We could equally agree that the price must be quoted in hexadecimal notation or whatever. Just a way to encode information. From an economic point of view what matters (i.e. what determines profit and loss) is the dirty or all-in price. At least that's what I was taught. (Though the original purpose of the convention does seem to have been a rough and ready way to make the chart look less jumpy). Dec 4, 2023 at 13:59
• Thank you very much @nbbo2 I think your last (bracketed) sentence is exactly what I was wondering about :)
– EE18
Dec 4, 2023 at 15:15