Is it a coincidence that the monthly payment equation includes both formulas to calculate compound interest and compound interest w/out the principal?

khodge

New member
Joined
Jun 26, 2019
Messages
1
Greetings all,

I have seen the derivation of the monthly payment equation (using series)

p= [Cr(1+r)^N]/[(1+r)^N-1]

where
C=principal
r=monthly rate
N=number of months
p=monthly payments

but is it a coincidence that the monthly payment equation includes both formulas to calculate compound interest and compound interest w/out the principal?
compound interest is C(1+r)^N and compound interest w/out the principal is C(1+r)^N-C. I can "build" the monthly payment equation using these but cannot justify the steps or make sense of each step. I've done research but can't find anything to support building this equation out of the formulas to calculate compound interest and compound interest w/out the principal.

Thanks for your help!
 
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