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From: stevev@tekchips.UUCP (Steve Vegdahl)
Newsgroups: net.invest
Subject: Re: amortization schedule?
Message-ID: <355@tekchips.UUCP>
Date: Sat, 9-Nov-85 01:09:16 EST
Article-I.D.: tekchips.355
Posted: Sat Nov  9 01:09:16 1985
Date-Received: Sun, 10-Nov-85 09:26:28 EST
References: <10800001@uicsl>
Organization: Tektronix, Beaverton OR
Lines: 75

> I have some questions about early payment of a loan.
> The solution certainly must be trivial to anyone who took accounting.
> 
> 1) I have a simple interest loan.
>    Interest is calculated on principle due at end of each month.
>    Principle P, Interest (annual) I, Months (terms) N
> 2) No penalty for early payment of any or all of the loan.

For simplicity, I will let "I" be the *monthly* interest in all my
discussion below.  I also assume that interest is compounded monthly, as
is common with mortgages.

<>

First, I will define the quantity S:
  S = P / ((1+I)^N - 1)

> Q1?) What is the formula for calculating the amortization schedule?
>      I.e., given P,I,N,  how do I calculate the monthly loan payment $D.

D = I*(P+S)

Example:
  P = $100,000
  I = 0.01 (i.e., 12% *annual* interest)
  N = 360 (i.e., 30-year loan)
 then
  S = 2861.259693
  D = 1028.612597

> Q2?) For payment, M (1<=M<=N), how do I calculate the amount of interest
>      (and/or principle) that makes up the loan payment of that month.
	
Amount that goes toward principal for payment M is
	I * S * (1+I)^(M-1)
The rest goes toward interest.

Example (continued):
  first month (M=1): 28.61259693 goes toward principal
  180th month (M=180): 169.8568962 goes toward principal
  300th month (M=300): 560.5934742 goes toward principal
  last month (M=360): 1018.428314 goes toward principal

> Q3?) If my loan payments are $D dollars per month and I pay $(D+X) on the
>      loan, can I calculate how much earlier the loan will be paid back?

To calculate N', the total number of months it will take to pay off the
loan if X dollars are added to each month's payment:
  N' = (log(P + S + X/I) - log(S + X/I)) / log(1+I)
This formula does not work for I = 0, but if there's no interest, but
that case is pretty uninteresting (pun intended).

Example (continued):
  Add $50 per payment: loan paid off in 263.1971688 months
  Add $100 per payment: loan paid off in 218.2781294 months
  Add $200 per payment: loan paid off in 169.0006103 months
  Add $1000 per payment: loan paid off in 68.25312833 months

The fractional months, of course, indicate that the loan will not be
paid of exactly; i.e., the final payment will be for some smaller residual
balance.

Doing this will, of course, cause the amount of principal (and interest)
paid each month to be different than calculated in (Q2).
  
> Q4?) Is this the correct spelling of 'principle'?

No.

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