Is it possible to solve for a negative exponent? If so, can someone help me get the n on one side of the equation?

I'm not a math student and I have no math teacher connections so I thought I would turn here when I was unable to find the answer myself on Google.

The equation calculates monthly car payments ($m$) from interest rate ($i$), principal ($p$) and number of months ($n$). I figured out how to solve for $p$ if I have all the other values. I assume $i$ is impossible to solve for, but $n$ looked like it might be possible.

?I'm not really sure about the math terms either if someone wants to help and put the correct tags.

$$\frac{\frac{i}{12}\times p}{1-\left(1+\frac{i}{12}\right)^{-n}} = m$$

  • $\begingroup$ If you know all the other values, you can find $n$, using logarithms $\endgroup$ – Henry May 3 '16 at 7:57
  • $\begingroup$ Any idea what that equation might look like? $\endgroup$ – Tyler May 3 '16 at 8:02
  • $\begingroup$ You could multiply both sides of the equation by the denominator in order to cancel it on the left side. Then, isolate the term with the $n$ on the right side, and take a logarithm of both sides. Then you can bring down the n and divide by the logarithm to completely isolate $n$ $\endgroup$ – Ovi May 3 '16 at 8:08


$a^{-b} = \frac{1}{a^b}$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.