Compound interest problem with increasing deposits An Investor starts with an initial investment : $A$
He earns a steady profit of 10 percent per year.
But every year he adds additional amount which increases by 15 percent every year.
At the end of first year he adds an amount $x$ 
That means he adds 1.15$x$ at the end of 2nd year. And adds $(1.15)^{n-1}x$  at the end of $n$th year
What is amount of funds after $n$ years, $n>2$ 

If the initial amount is $A$, at the end of the first year the money amount is $\frac{11}{10}A+x$.
At the end of the second year, the money amount is:
$$\frac{11}{10}\left(\frac{11}{10}A+x\right)+\frac{23}{20}x,$$
while at the end of the $n$-th year it is:
$$\begin{eqnarray*}A\cdot\left(\frac{11}{10}\right)^n  + x\cdot\sum_{k=1}^{n}\left(\frac{11}{10}\right)^k\left(\frac{23}{20}\right)^{n-k}&=&A\cdot\left(\frac{11}{10}\right)^n+x\cdot\left(\frac{23}{20}\right)^n\sum_{k=1}^{n}\left(\frac{22}{23}\right)^k\\&=&A\cdot\left(\frac{11}{10}\right)^n+22\,x\cdot\left(\frac{11}{10}\right)^n\left(\left(\frac{23}{22}\right)^n-1\right).\end{eqnarray*}$$
