Ok. I am trying to put together a 5-year revenue projection. I only have the following data:

• Units Sold in Year 1: 20
• Units Sold in Year 2: 80
• Units Sold in Year 3: 200

Now I need to use this data to figure out:

1. What monthly growth rate to use for each month from Year 1 to Year 5 to project monthly unit sales?
2. Similarly, growth rate to use for each quarter?
3. The 5-year compound annual growth rate?
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Are you going to assume that the growth rate is uniform throughout the five years, and that this uniform growth rate produced the given data? – Arturo Magidin May 16 '11 at 18:00
Just assume uniform throughout five years. Doesn't need to exactly match the growth rates in the provided data, but be based somewhat on it, if that makes sense. – keruilin May 16 '11 at 18:07
The annual growth from year 1 to year 2 is 300%, which would correspond to approximately 9.6% monthly growth. The annual growth from year 2 to year 3 is 150%, which corresponds to approximately 3.4% monthly growth. That's a pretty big difference, so that trying to approximate with a single growth rate is likely going to produce some horrible errors. – Arturo Magidin May 16 '11 at 19:30

As Arturo pointed out, using uniform growth here is probably not what was intended. Assuming that the growth rate halves every year seems more plausible. Also, the question 1 seems to indicate that you should find a different growth rate for each month (and hence quarter).

My intuitive answer would be the following:

Since the growth rate seems to halve every twelve months, use the formula for half-life:

$$g = g_{0} \left( \frac{1}{2} \right) ^{\frac{t}{12}}$$

where $g$ is your growth rate, and $g_{0}$ is your starting value of growth (in this case, 600) and $t$ is the time in months..

You can compute the compound rates from there.

Then again, this is just a gist. The question seems quite vague and leaves many room for different assumptions.

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