Bond Pricing Formula

[VanBuren77]

Hi -

I am a bit stumped on the algebra to go from this general sum of the bond pricing formula:

P(C,y,N,m) = P =

$\sum_{i=1}^{N} (C/m)(1+y/m)^i  + 1/(1+y/m)^N$

To:

C/y(1-1/(1+y/m)^N) + 1/(1+y/m)^N

Why does the sum become a "1 - "?

And if someone can help me figure out how to write latex on this forum that'd be great.

 

[Lu Shu Kai FRM]

Hi @VanBuren77 ,

Not sure if latex can be written on this forum. However, some thoughts on your formula -

The first formula makes sense. The second is actually a mathematical proof question with an identity that is required, which is:


Here is the proof (I ignored the principal payment because they are the same for both formulas):

Hope this is helpful!