Annual growth of vegetarianism?

Using an annual growth rate, how can I convert monthly revenue growth to quarterly revenue growth?

• Above you will see two numbers and their respective cell values. I have an annual growth rate of 16.303% which i divided by 12 to get the monthly growth rate. In the second file on the right I have the quarterly values. What I did was take the baseline revenue from month 1 on the right and multiplied it by 3 to get a baseline for quarter 1 on the right (Not sure if that was right, but it makes sense in my head). I then used 16.303% and divided by 4 for the quarters (Which I know is not right). I don't understand how businesses can included forecast growth with these HUGE differences in growth values between months, quarters, annual. How can I calculate it so it makes mathematical sense? I don't want to multiply by three through the entire four year forecast. Is there a decent formula to work with?

• Answer:

  Rather than multiplying and dividing the growth rate, you should apply exponents. Let's start with the basics. When something is growing at 1% monthly, each month you multiply the previous month's result by 1.01. Month 0 (start) = 1 - 1= 0% growth Month 1 = (1 * 1.01) - 1= .01 = 1% growth Month 2 = (1 * 1.01 * 1.01) - 1 = .0201 = 2.01% growth Month 3 = (1 * 1.01 * 1.01 * 1.01) - 1 = .030301 = 3.0301% growth And so on. A shorthand for representing this is through an exponent. (1.01 ^ 3) - 1 = (1.01 * 1.01 * 1.01) - 1 = .030301 = 3.0301% = The result of 3 months of growth at 1% monthly. This is similar but different from taking a growth rate and multiplying it by the number of months you're calculating. 1% * 3 months = 3%. Which is close to 3.0301% but not quite the same. This may sound like a small rounding error, but the difference between the two methods of computation grows astoundingly as the growth rate and exponent increase. For example, take 36 months of growth at 3% monthly growth. Exponent method: (1.03 ^ 36) - 1 = 1.89 = 189% growth Multiplication method: 3% * 36 = 108% growth Wow. Not even close. OK, so how do we switch over? It's fairly simple. Whatever you would have multiplied the growth rate by, insert an exponent instead. So when switching from monthly to annual growth, simply use an exponent of 12 instead of multiplying by 12. Moving from annual back to monthly is a little less intuitive, but just as easy once you get the hang of it. Just remember that dividing by something is the same as multiplying by its reciprocal. So dividing by 12 is the same as multiplying by 1/12. Thus, to move from annual back to monthly, use an exponent of 1/12. Here are a few examples of converting growth rates using exponents: Change 16% annual growth to a monthly growth rate: (1.16 ^ (1/12)) - 1 = 1.24% Change 1.5% quarterly growth to an annual growth rate: (1.015 ^ 4) - 1 = 6.14% Change 3% quarterly growth to a monthly growth rate: (1.03 ^ (1/3)) - 1 = 0.99% Good luck! Note: As per the comments, order of mathematical operations (BEDMAS) are extremely important in producing the correct output. Take care to use brackets to ensure things are being calculated in the correct order. E.g. 1.16^1/4 has a different result than 1.16^(1/4).