On morgage payments
Cameron Laird
claird at starbase.neosoft.com
Thu Oct 18 19:56:28 CEST 2001
In article <mailman.1003414106.5819.python-list at python.org>,
John Thingstad <john.thingstad at chello.no> wrote:
>Isaw earlier a very inefficient way of calculating morgage on a loan.
>The recurence relation:
>
>P = amount
>i = interest
>d = downpayment
>
>P = i*P - d
> n n-1
>
>was solver by itteration in a loop
>
>I would like to point out:
>
>P = i * (i*P - d) - d
> i+1 i
>
>P = i * ( i * (i * P - d) -d) -d)
> i + 2 i
>
>
>P = i*i*i*P -d(i^2 + i +1)
> i+2 i
>
>by inspecion i*i*i is a exponential and i^2 + i +1 is a geometric series so we have:
>
>P = i^n * P - d * (i^n -1 / i -1)
> n 0
>
>Which can be computed once.
>
>
I can't interpret what appears above in any standard way
to yield internally-consistent results. Rather than patch
up what I suspect is just mis-parenthesization, I offer
factor = (1 + i) ** n
payment = P * i * factor / (factor - 1)
as the most useful pertinent closed-form computation.
--
Cameron Laird <claird at NeoSoft.com>
Business: http://www.Phaseit.net
Personal: http://starbase.neosoft.com/~claird/home.html
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