# Applications of math - Root finding

Toby_Obie
Hello,

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

$$A = Pi/1-(1+i)^-n$$

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 any one 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 ?

## The Attempt at a Solution

pootette
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?

Toby_Obie
Yes, our teacher asked if it could be solved for i

All other values know

Thanks

pootette
What steps have you taken? I know we aren't supposed to give you the answer... But I will say it definately 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:
pootette
What steps have you taken? I know we aren't supposed to give you the answer... But I will say it definately 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...

Toby_Obie
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