MHB Why Does Changing Order of Rate Adjustments Affect the Final Outcome?

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Changing the order of rate adjustments affects the final outcome due to the use of different bases for each calculation. This concept is illustrated by the example of calculating 100 less 10% and then increasing the result by 10%, which does not return to the original number. The sequence of adjustments influences their impact, as later adjustments can have different effects compared to earlier ones. The discussion emphasizes that the calculations are not linear and depend on the order in which they are applied. Understanding this principle is crucial for accurate financial assessments.
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I am having a tough time figuring out why the change in the rates in this problem is not equal to the sum of the pieces, any assistance would be appreciated:

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Different Bases for each individual calculation.

It doesn't work for the same reason that the old trick question doesn't get you back where you started...

What is 100 less 10% and then the result is increased by 10%? Please respond to this question.
 
tkhunny said:
Different Bases for each individual calculation.

It doesn't work for the same reason that the old trick question doesn't get you back where you started...

What is 100 less 10% and then the result is increased by 10%? Please respond to this question.

Agree, but then the order of the adjustments would dictate the impact. Meaning the 4th adjustments will have one bases point impact as the last adjustment but a different impact as the first adjustment.

- - - Updated - - -

tkhunny said:
Different Bases for each individual calculation.

It doesn't work for the same reason that the old trick question doesn't get you back where you started...

What is 100 less 10% and then the result is increased by 10%? Please respond to this question.

99,
 

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Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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