Solve summation for variable that is in upper limit and summation I don't remember how to solve these, but I hope someone can refresh my memory.  I have the following equation, how can I solve for t?
$$50000 = \sum_{i=0}^{12t} 1.004^{12(t - i/12)}$$
EDIT: if it helps at all, expands out to $$50000 = 1.04^{12t} + 1.04^{12(t-1/12)} + 1.04^{12(t-2/12)} + .... + 1$$

$$\begin{align}
50000 
&= \sum_{i=0}^{12t} 1.004^{12(t - i/12)}
\\
&=\sum_{i=0}^{12t} 1.004^{12t - i}
\\
&=\sum_{k=0}^{12t} 1.004^k\qquad\text{where $k=12t-i$}
\\
&=\frac{1.004^{12t+1}-1}{1.004-1}
\\
1.004^{12t+1}&=201
\\
t&=\frac 1{12}\left(\frac{\ln 201}{\ln1.004}-1\right)=110.62\qquad\blacksquare
\end{align}$$
