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How to calculate annualised growth


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I wrote a piece on it here: https://www.offtopic.co.za/finance/how-to-calculate-annualised-growth

For added effect, here is a calculator: https://www.offtopic.co.za/finance/tools/annualised-growth-calculator

 

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Going to Google Finance and querying your favourite ETF or share and seeing it grew by 150% over the last 10 years is awesome! Why? Because 150/10 is 15% growth on average every year, right? No... unfortunately not. The 150% over 10 years is compound growth. So how do you work it out?

 

Step 1: First, you need the end value of the stock (in cents). Let's say R25.00 which is 2500. 

 

Step 2: Then you need the starting value of the stock: R10,00 (or 1000).

 

Step 3: Get the year fractional value of 1/[years]. So in this example, it will be 1/10 or 0.1

 

Step 4: Subtract the starting value from the current value and divide that by the starting value:

 

(2500 - 1000)/1000 = 1.5 (this we'll call your return rate)

 

Step 5: Now add 1 to the return rate and raise it by the year fractional value (calculated in Step 3) and subtract 1 from the result:

 

((1.5+1)^0.1)-1

 

Simplified it reads: (2.5^0.1)-1

Simplified some more: (1.0959)-1

And the result: 0.0959 (your annualised growth percentage). 

 

If you struggle to read it, multiply the number by 100: 9,59%

 

 

In Summary: 

 

Let's use real data - STX40 between 2 Jan 2004 and 30 Dec 2016 (13 years):

 

Starting value: 960

End value: 4382

Year fraction: 1/13 = 0.077

 

(4382-960)/960 = 3.56

 

((3.56+1)^0.077)-1 = 0.1239

 

Annualised growth: 12.39%

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So I'm decommissioning the offtopic.co.za site because I enjoy writing blogging software more than I do writing actual blog posts. BUT, I use that calculator a lot so if anybody is interested, I moved (and updated, read, mobile friendly) it over here:

 

https://andrev.me/growth-calculator/

 

On a side note, if anybody wants a domain called offtopic.co.za let me know - cheap cheap :D

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