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From: smh@mhuxl.UUCP (henning)
Newsgroups: net.consumers
Subject: Re: Bi-weekly mortgage repayments
Message-ID: <346@mhuxl.UUCP>
Date: Sun, 24-Nov-85 22:28:03 EST
Article-I.D.: mhuxl.346
Posted: Sun Nov 24 22:28:03 1985
Date-Received: Mon, 25-Nov-85 07:46:47 EST
References: <1389@decwrl.UUCP> <22100024@inmet.UUCP>
Organization: AT&T Bell Laboratories, Murray Hill
Lines: 30

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From the keys of Steve Henning, AT&T Bell Labs, Reading, PA mhuxl!smh

If r is the interest per payment period, x is the payment, n is the number of
payments and p is the principle Richard Schooler derived:

> 	x = p * r * (1 + 1 / ((1 + r)^n - 1)).
> 	n = log (1 + (p * r) / (x - (p * r))) / log (1 + r).

Note: these equations have problems with interest free loans where
	r=0, x=p/n, and conversely n=p/x
Since these are trivial cases, congratulations Rich on a fine solution.

>   If we now set x and r to half the previous amounts to model paying
> half a monthly payment twice a month, we get n = 718, or almost exactly
> 30 years, so we aren't saving much.  If we follow someone else's suggestion,
> and pay the half-monthly amount every two weeks, then this is equivalent
> to paying 13/12 ths the monthly amount every month, so x = $1114.33.
> Keeping r = .01, we get n = 228 months, or 19 years.

Carrying this one step further we find that for various interest rates we get:
r=  7%    8%    9%    10%   11%   12%   13%   14%   15%   
n= 23.73 22.85 21.92 20.96 20.00 19.04 18.08 17.19 16.13 years respectively
on a 30 year mortgage with 1/2 of the monthly payment paid biweekly.

Going one more step, for various year mortgages at 11% interest we get:
old n=  30 years  25 years  20 years  15 years  10 years
old x=  $952.32   $980.11   $1032.18  $1136.60  $1377.50
new n=  20.0 yrs  18.15 yrs 15.62 yrs 12.46 yrs 8.69 yrs respectively
on a 30 year mortgage where the new biweekly x is 1/2 of the old monthly x.