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The formula you provided is:

\[
Ag = G \left( \frac{1}{i} - \frac{n}{(1+i)^n - 1} \right)
\]

You want to solve for \( i \) (the interest rate). This equation appears to resemble a form of an annuity or loan amortization formula, where \( Ag \) represents an amount (like an annual payment), \( G \) is some constant or principal amount, \( i \) is the interest rate, and \( n \) is the number of periods.

Let's work through the steps to solve for \( i \):

### 1. Isolate the term involving \( i \)
First, divide both sides of the equation by \( G \):

\[
\frac{Ag}{G} = \frac{1}{i} - \frac{n}{(1 + i)^n - 1}
\]

Let’s denote this by:

\[
\frac{Ag}{G} = A
\]

Thus, the equation becomes:

\[
A = \frac{1}{i} - \frac{n}{(1 + i)^n - 1}
\]

### 2. Combine terms
Now, let’s bring all terms involving \( i \) on one side and isolate the constant terms on the other side. This step involves some algebraic manipulation, and solving for \( i \) explicitly may require numerical methods because the equation is not easily solvable in a closed form. However, we can express the process needed for solving it.

Would you like me to attempt a numerical solution for a specific value of \( A \), \( n \), or \( G \), or should I continue the algebraic derivation process?

Additionally, feel free to provide any missing values so I can calculate \( i \) for you.

This page provides a step-by-step solution to solving the annuity formula for the interest rate i. The formula Ag = G(1/i - n / [(1 + i)^n - 1]) is used in financial mathematics to calculate payments. This solution is suitable for students at the undergraduate level.

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