Applications of math - Root finding

In summary, the person is asking for help on a homework question involving a formula from finance. They say that it can be solved for i, but they've had no luck with replacing i with known values. They're also asking about how to solve for i, but they don't specify what root finding algorithm they would use.
  • #1
Toby_Obie
19
0
Hello,

I came across the following formula after asking for practical applications of math in finance and other sciences, it concerns mortgage payments

[tex]A = Pi/1-(1+i)^-n[/tex]

The above denominator end part reads (1+i)^(-n)

As a mathematical question, is it possible to rearrange the equation to find i ?

Wikipedia says

One can rearrange the formula to solve for anyone term, except for i, for which one can use a root-finding algorithm.

Is there a way of doing this ? What root finding algorithm would be used ?

Thanks for your help
 
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  • #2
A few of questions:
1. Is this related to a homework question?
2. Is it safe to assume you have quantities for all variables except for i?
3. Have you tried to interpolate yet?
 
  • #3
Yes, our teacher asked if it could be solved for i

All other values know

Thanks
 
  • #4
What steps have you taken? I know we aren't supposed to give you the answer... But I will say it definitely can be done... just not extremely simple to do.

For what reason are you solving for i? Just to solve for it? Or are we trying to find the value for i given an annuity and a principle investment over a given number of years?
 
Last edited:
  • #5
pootette said:
What steps have you taken? I know we aren't supposed to give you the answer... But I will say it definitely can be done... just not extremely simple to do.

For what reason are you solving for i? Just to solve for it? Or are we trying to find the value for i given an annuity and a principle investment over a given number of years?

That formula looks eerily similar to capital recovery and uniform series present worth:

A= P*[(i(1+i)n)/((1+i)n-1)] and P=A*[((1+i)n-1)/(i(1+i)n)] respectively...
 
  • #6
Hello,

The formula comes from finance, however the question was posed from a purely mathematical point of view, how do we solve for i ?

Rearranging comes to now avail, I tried replacing i in terms of known values (from other equations) but no outcome

How would I go about solving for i, apparently the answer lies in a "root finding algorithm", but what could I use ?

Thanks
 

1. What is the purpose of root finding in math applications?

Root finding is used to determine the roots or solutions of a mathematical equation or function. This is important because it allows us to find the values or points where the equation is equal to zero, which can have significant real-world implications in fields such as engineering, economics, and physics.

2. What are some common methods used for root finding in math applications?

There are several methods for root finding, including the bisection method, Newton's method, and the secant method. These methods vary in complexity and efficiency, and the best method to use depends on the specific equation or problem being solved.

3. How does root finding relate to optimization problems?

Root finding can be used to solve optimization problems, where the goal is to find the minimum or maximum value of a function. This is done by finding the roots of the derivative of the function, which represents the points where the function is either increasing or decreasing. The optimal solution can then be found at the root of the derivative.

4. What are some real-world applications of root finding?

Root finding has many practical applications, such as determining the optimal dosage of medication, calculating the trajectory of a rocket, and finding the break-even point for a business. It is also used in financial modeling, image processing, and data analysis.

5. What are some challenges associated with root finding in math applications?

One common challenge is that some equations may not have a closed-form solution, meaning there is no algebraic expression for the roots. In these cases, numerical methods must be used, which can be time-consuming and may not always provide an exact solution. Another challenge is that some equations may have multiple roots, and it can be difficult to determine which root is the correct one for a given problem.

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