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From: laird@chinet.chi.il.us (Laird J. Heal)
Newsgroups: alt.sources.wanted
Subject: Re: mortgage program
Message-ID: <1991Jan04.112213.5193@chinet.chi.il.us>
Date: 4 Jan 91 11:22:13 GMT
References: <9101022144.AA13152@hp370b.CFSMO.Honeywell.COM> <1991Jan3.194905.247@ee.rochester.edu>
Organization: Chinet - Public Access UNIX
Lines: 50

>Does anyone has a source program for mortgage payment calculations?  I like
>to run it on my IBM PC...please e-mail the program...thanks!

Well, I make a habit of deriving the formula every so often - not on the net
before, so here goes:

P=principal, n=number of payments, i=interest, x=payment:

month Principal Interest  payment new Principal
1     P         iP        x       P+iP-x
2     P-iP+x    i(P+iP+x) x       P+iP-x+i(P+iP-x)-x
                iP+(i**2)P-ix     P+2iP+(i**2)P-ix-2x
3     P+2iP+(i**2)P-ix-2x
                iP+2(i**2)P+(i**3)P-(i**2)x-2ix
				          x
                                  P+3iP+3(i**2)P+(i**3)P-(i**2)x-3ix-3x
                                  P(1+i)**3-((i**3)x+3i(**2)x+3ix)/i
                                  P(1+i)**3-((i**3)x+3i(**2)x+3ix+x - x)/i
                                  P(1+i)**3-((i+1)**3) - 1)x/i

and unless you misbelieve the patterns,
to set "new Principal" to zero after n
months, we have to set
P(1+i)**n=((i+1)**n) - 1)x/i
and
x = Pi((1+i)**n)/(((1+i)**n) - 1)
which can be further reduced, by means of
such modern tools as pencil and paper, to

x=Pi(1/(1-(1/(1+i)**n)))

in order to only make one exponentiation.

Well, I didn't write the program for you (I usually just
use a pocket calculator) but the only thorny problem is
really the one:  given the monthly payment I can afford
and the price/interest-rate I am facing, how long will
it take to make to payoff?

as x=Pi((1+i)**n)/(1 - (1+i)**n)
   x - x(1+i)**n = Pi(1+i)**n
   x=(Pi+x)(1+i)**n
   x/(Pi+x)=(1+i)**n
   n=(log(x/(Pi+x)))/log(1+i)

Now maybe if I get really ambitious I will put together
a little bit of scanf() and printf() and...nah.
-- 
Laird J. Heal                           The Usenet is dead!
Here:  laird@chinet.chi.il.us		Long Live the Usenet!