*Originally posted by geepamoogle*

**M = P * i / [1 - (1+i)^-n]
**

M = monthly payment

P = Current principle

i = monthly interest rate (In this case, 5% / 12)

n = number of monthly payments

If we let x = 1+i, then the expression becomes:

M = P * (x-1) / [1 - x^n]

Rearranging, we have:

M/P * [1 - x^n] = (x-1)

Multiplying both sides by x^n and factoring out (x-1) from the left hand side, we have:

M/P * (x-1) * [x^n - x^(n-1) + x - 1] = x^n * (x-1)

Cancelling (x-1) from both sides, we're left with:

M/P [x^n - x^(n-1) + x -1] = x^n

Rearranging into polynomial form, we have:

(1-M/P) * x^n + x^(n-1) - x + 1 = 0

Now, the fundamental theorem of algebra states that "every non-constant single-variable polynomial with complex coefficients has at least one complex root." However, the Abel-Ruffini theorem also states that "there is no general solution in radicals to polynomial equations of degree five or higher."

http://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra

http://en.wikipedia.org/wiki/Abel's_impossibility_theorem

So, the solution must exist, and a specific equation may exist to solve it, but there is no general formula for producing the result (provided n>4, which is usually the case for a mortgage ðŸ˜‰). I suppose this is just a long-winded way of saying approximation is the best method in this case.