# Incremental Percentage Increase (20 steps) Does Not Equal Lower Range Number to End Range Number

• I have a range of numbers 7150 - 9150 (2000 difference)
• Between that range, I am incrementing by 100.
• I am calculating the percentage increase at each of the incremental increases.

The total range percentage increase 9150-7150/7150 does not equal the sum of the incremental percentages. See Attached Image.

More perplexing. - I am taking each incremental % change and multiplying by 3. So 1% becomes 3%, etc. - The SUM of the new percentage is around 74% (see image) - Incrementally also I am taking that new percent and calculating the rise in a number starting at the value of 60. (see image) - The final total of that new number go from 60 to 124 with a percent rise of 107%.
- This is way off from 74%.

Somewhere my calculations are awry.

Thank you for any help in comprehending these phenomena. I tried to spell out exactly what my calculations are in the attached image.enter image description here

Range   Percent Change  Original Percent * 3    Percent Applied To Value
7150                                                  60
7250    1.398601399%    4.19580420%                   62.51748252
7350    1.379310345%    4.13793103%                   65.10441283
7450    1.360544218%    4.08163265%                   67.76173580
7550    1.342281879%    4.02684564%                   70.49039630
7650    1.324503311%    3.97350993%                   73.29133920
7750    1.307189542%    3.92156863%                   76.16550937
7850    1.290322581%    3.87096774%                   79.11385167
7950    1.273885350%    3.82165605%                   82.13731096
8050    1.257861635%    3.77358491%                   85.23683213
8150    1.242236025%    3.72670807%                   88.41336004
8250    1.226993865%    3.68098160%                   91.66783955
8350    1.212121212%    3.63636364%                   95.00121553
8450    1.197604790%    3.59281437%                   98.41443286
8550    1.183431953%    3.55029586%                  101.90843639
8650    1.169590643%    3.50877193%                  105.48417100
8750    1.156069364%    3.46820809%                  109.14258156
8850    1.142857143%    3.42857143%                  112.88461292
8950    1.129943503%    3.38983051%                  116.71120997
9050    1.117318436%    3.35195531%                  120.62331757
9150    1.104972376%    3.31491713%                  124.62188058

28%           24.82%         74.45%                       107.70%

(9150-7150)/7150=28%    SUM(J4:J24)=24.82%  SUM(K4:K24)=74.45%  124-60/60=107%

7250-7150/7150=1.39%    0.013986014
1.39%*3=4.19%   0.041958042

124-60/60=107%  1.077031343

28% * 3 <> 107% Calculations Way Off
24.8% * 3 <> 107%   Calculations Way Off


The reason is that the first change is relative to the first value, but the second change is relative to the second value, and so on. Even if there were only three numbers, that sum is meaningless. In other words, using the example with three numbers $$a<b<c$$ note that $$\frac{b-a}{a} + \frac{c-b}{b}\neq\frac{c-a}{a}$$