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Here is the annuitet payment formula: $$p = s \cdot \left(r + \frac{r}{(r+1)^t-1}\right)$$

Is it possible to solve it for rate ?

gt6989b
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Homer
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  • i don't think there is an analytic solution, especially for non-integer $t$, but you can certainly use a root-finder to solve numerically – gt6989b Apr 11 '19 at 10:34
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    Have a look at https://math.stackexchange.com/questions/1536653/approximating-the-compond-interest-for-a-loan/1545603#1545603 – Claude Leibovici Apr 11 '19 at 11:49

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You have $$ \begin{split} \frac{p}{s} = \frac{r(r+1)^t}{(r+1)^t-1} = \frac{r}{1-(r+1)^{-t}} \end{split} $$ so for general real $t$, no analytic solution would exist, this is a transcendental equation (kind of like solving $xe^x = c$).

But the RHS is a nice function for $r > 0$, you can certainly solve the equation numerically using a root-finder, like Newton's or Bisection methods.

gt6989b
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