Need help formulating an equation

[czar13]

I am a finance student and am having trouble formulating an equation to figure simple math over multiple years. I will give an example below.

I begin with a market size of 100,000 in year one which is multiplied by the market share of 5% which remains constant. So far this equals 5,000 equaling demand. This is then multiplied by $400 which is the selling price yielding $2,000,000 gross profit. To make things simple I'm currently just trying to solve for three years where the market size grows 5% a year. I can figure this by (1+growth rate)^n-1; however this only yields the gross profit for year 3. I need a formula that will yield the gross profit for the sum of all the years as shown below.

year 1= 100,000*.05=5000*400=2,000,000
5% growth
year 2 = 105,000*.05=5250*400=2,100,000
5% growth
year 3=110,250*.05=5512.50*400=2,205,000
so the answer is 2,000,000+2,100,000+2,205,000=6,305,000
as noted my growth equation can yield 2,205,00, but I cannot make the formula sum all the years gross profits. Please help. I have been at this for 6 hours now and cannot figure it out. Thanks in advance, Chris

 

[NateTG]

If I understand correctly, you want something like:

$$\sum_{i=0}^{n} r^i=\frac{1-r^{n+1}}{1-r}$$

(Where $$r$$ is the growth rate plus 1 and $$n$$ is the number of years minus 1.)

For more on this:
http://mathworld.wolfram.com/GeometricSeries.html