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February 25th, 2016, 06:42 AM   #1
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difference between a percentage increase each year and total change

I am trying to explain why there is a difference between a percentage increase happening each year between two dates and then when comparing the overall increase. For example

1980 - £25,000 sales;
1981 - £26,000 sales; = 4% increase
1982 - £27,000 sales. = 3.85% increase

When adding up the yearly increase it comes to 7.85%, but the difference between the 1980 number and the 1982 number is 8%. I know why this happens, but I need to explain why in very simple language, so anyone accessing a file can understand!
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February 25th, 2016, 07:28 AM   #2
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You cannot add averages like that when they have different bases.
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February 25th, 2016, 07:29 AM   #3
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Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics
Quote:
Originally Posted by marenello99 View Post
I am trying to explain why there is a difference between a percentage increase happening each year between two dates and then when comparing the overall increase. For example

1980 - £25,000 sales;
1981 - £26,000 sales; = 4% increase
1982 - £27,000 sales. = 3.85% increase

When adding up the yearly increase it comes to 7.85%, but the difference between the 1980 number and the 1982 number is 8%. I know why this happens, but I need to explain why in very simple language, so anyone accessing a file can understand!
Overall growth factor = 1.04 * 1.0385 = 1.08004

The overall increase is thus 8.004%.
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February 25th, 2016, 09:46 AM   #4
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Google "compounding interest"
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February 27th, 2016, 04:10 PM   #5
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80-81 growth factor = 26000 ÷ 25000 = 1.04 or a 4% increase.
81-82 growth factor = 27000 ÷ 26000 ≈ 1.385 or a 3.85 % increase.

80-82 growth factor = 27000 ÷ 25000 = 1.08 or an 8% increase.

Denis, how does compounding interest relate to this problem? This problem is about sales increase. There is no interest involved.

Last edited by Timios; February 27th, 2016 at 04:13 PM.
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February 27th, 2016, 05:45 PM   #6
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SAME THING!

25000 increases to 27000 over 2 years:
25000(1+i)^2 = 27000
(1+i)^2 = 27/25
1 + i = sqrt(27/25)
i = sqrt(27/25) - 1 = .03923...~3.92%

That is the result of 4%, then 3.85%.
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February 29th, 2016, 12:26 AM   #7
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"Compund Interest" is an unfortunate term, it should really be called compound percentage to cover the general use. Recursive multiplication would be even better
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