I have been searching for a way to solve for the interest rate given the monthly payments of a loan. I would like to set up a problem as the following.
$X$=monthly payment , $i$=effective interest rate for each month, $n$=the total number of payments to pay off the loan. Assume that one borrows $1$ as a loan.
I understand that the following is true
$$Xa_{\overline{n}\rceil i}=1$$
or in other words,
$$\frac{1-(1+i)^{-n}}{i}=\frac{1}{X}$$
Here, solving for one variable given the other two seems like an easy problem, but to me that is the case only for solving for $n$ and $X$.
I tried to search for a way to solve for $i$, and I was wondering how these types of problems are solved in the exam FM. I understand that a graphing calculator is not allowed, I am thinking that there must be a way to solve this by hand.
Can I have some input?
Thanks.