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# Hi, how do you calculate growth rate for next three years knowing annual growth (%)?

We are looking at a market with 520M items in 2012 and want to know how big it will be in 2015. We know that growth rate from 2011-2012 was 4.7% and can assume the same for the next three years. I see here the result is 602M, so the 520M was multiplied by 1.05(to the power of three), but don't know why. What is the formula you use to calculate growth like this?

Thank you.

We are looking at a market with 520M items in 2012 and want to know how big it will be in 2015. We know that growth rate from 2011-2012 was 4.7% and can assume the same for the next three years. I see here the result is 602M, so the 520M was multiplied by 1.05(to the power of three), but don't know why. What is the formula you use to calculate growth like this?

Thank you.

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Increasing by 4.7% (approximated to 5%) is equal to multiply the initial value by 1.047 (approx 1.05).
Since this occurs three years in a row (from 2012 to 2015) you multiply the initial value by 1.05, then that value by 1.05 again for the second year and a third time for the third year.
This leads to ((520*1.05)*1.05)*1.05 leading to 520*1.05**3 (**3 means to the power of three).

Increasing by 4.7% (approximated to 5%) is equal to multiply the initial value by 1.047 (approx 1.05).
Since this occurs three years in a row (from 2012 to 2015) you multiply the initial value by 1.05, then that value by 1.05 again for the second year and a third time for the third year.
This leads to ((520*1.05)*1.05)*1.05 leading to 520*1.05**3 (**3 means to the power of three).

Exact formula is: Initial Size x ( 1 + growth rate)^n where n is the number of periods.

In this case \$520m x ( 1+ 0.047)^3 where 3 is the number of years, 520m is the initial market size, and 0.047 is the growth rate.

Since this exact calculation is hard to do without a calculator, you round the 4.7% (or 0.047) to 5.0% (or 0.05), and adjust the formula to the following: \$520m ( 1 + 0.05 x 3), or \$520 x 1.15, which comes out to \$598m. This is just the standard way of making the formula manageable without a calculator, but beware that the more periods you are using this estimate over, the more your answer will be underestimated.

Note that if the market was shrinking instead of growing, you'd just make the growth rate negative.

Hope this helps!

Exact formula is: Initial Size x ( 1 + growth rate)^n where n is the number of periods.

In this case \$520m x ( 1+ 0.047)^3 where 3 is the number of years, 520m is the initial market size, and 0.047 is the growth rate.

Since this exact calculation is hard to do without a calculator, you round the 4.7% (or 0.047) to 5.0% (or 0.05), and adjust the formula to the following: \$520m ( 1 + 0.05 x 3), or \$520 x 1.15, which comes out to \$598m. This is just the standard way of making the formula manageable without a calculator, but beware that the more periods you are using this estimate over, the more your answer will be underestimated.

Note that if the market was shrinking instead of growing, you'd just make the growth rate negative.

Hope this helps!

Additional question, you seem to be using a trick to convert the ^3 into something easy to use. Is there a rule for that? How would you do let's say 0.05^8? — Anonymous A on Sep 16, 2019

You basically move the 8 into the parenthesis like I did with the 3, so in your example the formula would be \$520m x ( 1 + 0.05 x 8), or \$520m x 1.4 What you have to be aware of is that over such a relatively extended number of years, this estimation becomes smaller and smaller relative to the answer you'd get using the exact formula. An example is a BCG practice test I did where one of the answer options was exactly the answer I obtained from my estimation (interestingly was also 8 years), so I picked it, and I was wrong because after 8 years I should know my estimate is less than the exact size of the market after 8 years, so I should pick an answer that is above my estimate, not the one that is exactly my estimate. Let me know if I wasn't clear enough! — Ignacio on Sep 16, 2019

Hello Johana,

Growth 2011-2012 = 4.7% for simplicity = 5%

We have 3 years horizon, so market in 2013 = market in 2012*1.05 = 520M*1.05and so on.

For 3 years= 520*1.05*1.05*1.05= 520*1.05^3= 602M

Cheers,

Hello Johana,

Growth 2011-2012 = 4.7% for simplicity = 5%

We have 3 years horizon, so market in 2013 = market in 2012*1.05 = 520M*1.05and so on.

For 3 years= 520*1.05*1.05*1.05= 520*1.05^3= 602M

Cheers,