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February 25th, 2016, 05:42 AM  #1 
Newbie Joined: Feb 2016 From: London Posts: 1 Thanks: 0  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  Â£25,000 sales; 1981  Â£26,000 sales; = 4% increase 1982  Â£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! 
February 25th, 2016, 06:28 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,107 Thanks: 854 
You cannot add averages like that when they have different bases.

February 25th, 2016, 06:29 AM  #3  
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics  Quote:
The overall increase is thus 8.004%.  
February 25th, 2016, 08:46 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,130 Thanks: 801 
Google "compounding interest"

February 27th, 2016, 03:10 PM  #5 
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 371 Thanks: 68 
8081 growth factor = 26000 Ã· 25000 = 1.04 or a 4% increase. 8182 growth factor = 27000 Ã· 26000 â‰ˆ 1.385 or a 3.85 % increase. 8082 growth factor = 27000 Ã· 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 03:13 PM. 
February 27th, 2016, 04:45 PM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,130 Thanks: 801 
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%. 
February 28th, 2016, 11:26 PM  #7 
Senior Member Joined: Apr 2014 From: UK Posts: 865 Thanks: 314 
"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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change, difference, increase, percentage, total, year 
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