Formula needed for summation I am not quite sure that the title is correct for the following scenario:
I have to pay a yearly maintenance fee A, but this fee increases by 5% each year (this is a fixed rate), so on my second year I pay A + 0.05xA or A(1+0.05) or Ax1.05. In year n, I would have to pay A multiplied by 1.05 to the power of (n-1).
So:
In Year 1 I pay A, In Year 2 I pay A x 1.05, In Year 3 I pay A x 1.05 to the power of 2, ... , In Year n I pay A x 1.05 to the power of (n-1).
I am not quite sure that the above formulas are correct, I did my best, but I'm not a mathematician.
I would need a formula that would add up the maintenance fees accumulated over the years, that is how much I paid in total over n years, considering the yearly increase of 5%. That is Year 1 + Year 2 + Year 3 + ... + Year n
Please help. Thank you in anticipation.

To give a short answer, the total payment is (with $q=1.05$)
$$ A\cdot \frac{q^n-1}{q-1}=20A(q^n-1).$$
The formula is well-known for compound interest as this.
