sum of constant percentage increase

Question

I don't remember the formula for adding up (n) numbers that are constantly increasing at a certain percentage. Example if n=3, that means adding up 3 years: year 1 = 100 year 2 = 100 * 1.03 = 103 year 3 = 100 * 1.03 * 1.03 = 106.09 total = 309.09

Answer 1

This is the sum of a geometric progression:

$$a + ar +ar^2+\dots+ar^n=a{r^{n+1}-1\over r-1}$$

In your example, $a=100, r=1.03, n=2$