Question

What is the formula for a finite geometric series and how can use it in a practical situation

Answer 1

The sum $S_{n}$ of n terms of a geometric series with first term $a_{1}$ and common ratio $r$ is given by

$S_{n}=a_{1}\cdot \dfrac{r^{n}-1}{r-1}$

It can be used in any situation involving the accumulated consequences of exponential growth. In finance, it is used to find the future value of a sequence of payments subject to compound interest.

For example, consider 10 deposits of 1000 made at the end of the year into an account paying 2% compounded annually. The result of such a sequence of payments will be

$S_{10}=\ 1000\cdot \dfrac{1.02^{10}-1}{1.02-1}=\ 10,949.72$