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Can someone help with rearranging the following formula to find n with explanation?

$$PMT = \frac{PV}{\frac{1}{r} \cdot(1- \frac{1}{(1+r)^{n}})}$$

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You use the notion of a logarithm to extract exponent, since $\log(a^n)=n\log(a)$. First we wish to isolate the $(1+r)^{-n}$ algebraically to get

$$1-\frac{rPV}{PMT}=(1+r)^{-n}$$ and then we apply the logarithm to get

$$\log\left(1-\frac{rPV}{PMT}\right)=-n\log(1+r)$$ and so we wind up at

$$n=-\frac{\log\left(1-\frac{rPV}{PMT}\right)}{\log(1+r)}$$

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  • $\begingroup$ Thanks Stella. Quick response. helps alot. $\endgroup$ – Morph777 May 4 '17 at 7:38
  • $\begingroup$ @Morph777 No problem! Welcome to the mathematics stack exchange. When you find answers helpful, you should click the up arrow next to them to award a point to the answerer. You can also accept an answer to your question by clicking the check mark beneath the up and down arrows $\endgroup$ – Stella Biderman May 4 '17 at 7:42

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