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From: stevev@tekchips.UUCP (Steve Vegdahl)
Newsgroups: net.math,net.invest
Subject: Re: Trivial Interest-Calculation Formula Needed
Message-ID: <356@tekchips.UUCP>
Date: Sat, 9-Nov-85 01:42:40 EST
Article-I.D.: tekchips.356
Posted: Sat Nov  9 01:42:40 1985
Date-Received: Sun, 10-Nov-85 09:26:42 EST
References: <719@hou2e.UUCP>
Distribution: net
Organization: Tektronix, Beaverton OR
Lines: 41
Xref: watmath net.math:2500 net.invest:858

> I posted this request in net.invest but got no response (yet), so I'll
>try here on net.math.   This should be duck-soup for this group !
>
> I am writing a spread-sheet program to calculate present and future return
>on investment properties.  I would like a formula which gives the
>total-interest paid to-date on a current loan with monthly payments.

Let
 P = principal
 I = *monthly* interest rate (i.e., annual interest rate divided by 12)
 N = term of the loan in *months*

Define
  S = P / ((1+I)^N - 1)

The amount paid toward the principal after M monthly payments is
  Q(M) = (S * (1+I)^M) - S

The monthly payment is
  D = I*(P+S)

Thus, the total interest paid after M monthly payments is
  total off all payments - total amount that went toward principal
    = M*D - Q(M)

Example:
  P = 100000
  I = 0.01 (i.e., 12% *annual* interest)
  N = 360 (i.e., 30-year loan)
  M = 50 (i.e., we want to know total interest paid through 50 months)
 then
  S = 2861.259693
  Q(M) = 1844.459048
  D = 1028.612597
 so the total interest paid is
  (M*D)-Q(M) = 51430.62985 - 1844.459048 = 49586.1708

		Steve Vegdahl
		Computer Research Lab.
		Tektronix, Inc.
		Beaverton, Oregon