Equation Solving with Newton-Raphson Method
Date: 07/23/2004 at 14:04:00 From: Steve Subject: Simplifying an Equation Hello Dr. Math! The equation for a future worth (F) given a uniform series payment (A), an interest rate per period (i), and (n) number of periods is: F = A*(((1+i)^n) - 1)/i Is there a way to solve this equation for i, such that we have i = ...? I am having trouble combining the two i's into one i. I'm thinking of natural logs, but seem to get stuck there.
Date: 07/23/2004 at 14:56:58 From: Doctor Korsak Subject: Re: Simplifying an Equation Hello Steve, There is no so-called "closed form" solution for i in terms of the other parameters; however, you can iterate towards a solution using something like the Newton's Method algorithm (often called Newton- Raphson). Define a function like f(i) = A*(((1+i)^n) - 1)/i - F and then solve the equation f(i) = 0 by starting out with a trial value like i = 0.1 and then iterating towards a solution to your desired accuracy. Many hand-held calculators have a button for this kind of operation. Take a look at a couple of the Dr. Math library archives on this subject: Cow Grazing Half the Circle: Newton-Raphson Method http://mathforum.org/library/drmath/view/53622.html Determining Roots of a Function http://mathforum.org/library/drmath/view/62610.html Please write back if you need further help. - Doctor Korsak, The Math Forum http://mathforum.org/dr.math/
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