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Path: utzoo!linus!philabs!prls!amdimage!amdcad!cae780!gordon
From: gordon@cae780.UUCP (Brian Gordon)
Newsgroups: net.invest
Subject: Re: A penny saved...
Message-ID: <1443@cae780.UUCP>
Date: Wed, 9-Oct-85 14:28:12 EDT
Article-I.D.: cae780.1443
Posted: Wed Oct  9 14:28:12 1985
Date-Received: Sat, 12-Oct-85 05:12:40 EDT
References: <161@aplvax.UUCP> <12073@rochester.UUCP>
Reply-To: gordon@cae780.UUCP (Brian Gordon)
Distribution: net
Organization: Tektronix, Inc. (CAE Systems Division), Sunnyvale, CA
Lines: 54

In article <12073@rochester.UUCP> bukys@rochester.UUCP (Liudvikas Bukys) writes:
>Most car loans are set up so that early payment of the entire balance
>of principal saves you little in interest.  If you read your contract,
>you will find something along the lines of "Calculation of interest due
>is subject to the well-known accounting `Rule of Sevens'", or something
>like that.  It might be the "rule of nines".  The upshot is that you
>owe most of the interest even if you pay the balance early.

You are presumably thinking fo the "Rule of 78's".  It's not that different
from "normal" amortization, at least for typical numbers.  People always
have problems computing it, but it isn't complicated.  The 78 comes from the 
specific numbers involved in a one year loan.  The computations go as follows.
Suppose the interest you are paying on a one year loan is $X.  How much of a
given payment goes towards principal, and how much towards the interest?
You could claim 1/12 of it was due each month, or allocate it "perfectly" as 
proportionate to the amount of principal left ("normal" amortization), etc.  
The Rule of 78's allocates it so that it is mostly due in the first few months 
by using the months left over the sum of the months.  In the one year case, 
the sum of the months is 1+2+3+..+12=78.  12/78 of the interest is assumed due 
the first month, 11/78 of it the second, etc., until the last 1/78 is due the 
last month.  

For $1,000 at 18% for 12 months, a simple amortization calls for a total of
$100.16 in interest (monthly payments of $91.68).  Comparing three methods of 
allocation:

      Simple interest
Month	Amortized	Rule of 78's	1/12
  1        15.00	    15.41	8.35
  2        13.85	    14.13	8.35
  3	   12.68	    12.84	8.34
  .	     .		      .		 .
  .	     .		      .		 .
 11	    2.69	     2.57	8.35
 12	    1.35	     1.28	8.34

As a borrower, if I pay off after just one month, I'd like to see all but
$8.35 of the first payment counted towards principal, but that isn't fair
to the lender.  Before the advent of computers/calculators/etc., figuring 
the simple-interest amortization schedule was a pain, and the Rule of 78's
isn't too bad an approximation, and is much easier to compute.  Paying off
two months early?  Knock off 3/78 of the total interest ...

FROM:   Brian G. Gordon, CAE Systems Division of Tektronix, Inc.
UUCP:   tektronix!teklds!cae780!gordon
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