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Path: utzoo!linus!decvax!genrad!grkermit!masscomp!clyde!ihnp4!ihlpf!dap1
From: dap1@ihlpf.UUCP (darrell plank)
Newsgroups: net.math
Subject: Figuring equiv. interest rates - (nf)
Message-ID: <227@ihlpf.UUCP>
Date: Thu, 1-Dec-83 03:00:38 EST
Article-I.D.: ihlpf.227
Posted: Thu Dec  1 03:00:38 1983
Date-Received: Fri, 2-Dec-83 07:21:25 EST
Organization: AT&T Bell Labs, Naperville, IL
Lines: 24

#N:ihlpf:6200020:000:987
ihlpf!dap1    Nov 30 22:10:00 1983

I was trying to figure out the "equivalent interest" I have been earning
in our savings plan here at ATT-BTL.  In other words, I have put in a
certain amount of money each month and at the end of N months I have X
dollars.  What constant compounded interest would have given the same
yield?  It seemed like it ought to be real easy, but after about a second
it became plain that a N'th order polynomial was involved.  I then thought
that it might be easier if I had made the SAME payments each month.  After
about another second, it was obvious that what I needed to solve was:

(SUM(i = 0 to N) X**i ) = A.

This is equivalent to

       X**(N+1) - AX + A - 1 = 0.

Is there some easy way to solve this, or do accountants have to resort to
numerical analysis whenever they want this kind of figure?

                                                   Thanks,
                                                   Darrell Plank
                                                   ihlpf!dap1