Bond Pricing Formula

VanBuren77

New Member
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 =
Markdown (GitHub flavored):
$\sum_{i=1}^{N} (C/m)(1+y/m)^i  + 1/(1+y/m)^N$

To:

Markdown (GitHub flavored):
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.
 

lushukai

Well-Known Member
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:
1635664418766.png

Here is the proof (I ignored the principal payment because they are the same for both formulas):
1635693292247.png
Hope this is helpful!
 
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