I'm trying to solve the following equation:
\begin{align} 100.474 &= \frac{1\cdot 1000}{\left(1+18.94833392\right)} +\frac{1\cdot 1000}{\left(1+5.3028 \right)^ 2}+\\ &\frac{1000\cdot 1}{\left(1+3.29905 \right)^ 3}+\frac{1000\cdot 1}{\left(1+2.55048 \right)^ 4}+\\ &\frac{1000\cdot 1}{\left(1+2.16545 \right)^ 5}+\frac{1000\cdot 1}{\left(1+1.93226 \right)^ 6}+\\ &\frac{1000\cdot 1}{\left(1+1.77628 \right)^ 7}+\frac{1000\cdot 1}{\left(1+1.66477 \right)^ 8}+\\ &\frac{1000\cdot 1}{\left(1+1.58115 \right)^ 9}+\frac{1000\cdot 1}{\left(1+1.51614 \right)^{10}}+ \frac{1000\cdot 1+1000}{\left(1+x\right)^{15}} \end{align}
However, my Wolfram Alpha is refusing to cooperate. Am I doing something wrong or is Wolfram Alpha just unable to solve it? If so, could you please point me to a different calculator?
Here is the link to my calculations in WA:
Thanks
You don't need software to solve the equation. It is of the form $$A = B + \frac{2000}{(1+x)^{15}},$$ where $A, B > 0$ are constants independent of $x$, defined by the sums you have above. The solution is $$x = \left(\frac{2000}{A-B}\right)^{1/15} - 1.$$