Question 1158324
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<pre>

If {{{r[1]}}}, {{{r[2]}}}, {{{r[3]}}}, . . . , {{{r[6]}}} are percentage rates increase/decrease, then the new price after a chain of changes is

    
    {{{P[new]}}} = {{{P[old]*(1+r[1])*(1+r[2])*(1+r[3])*ellipsis*(1+r[6])}}}.


What is INTERESTING, after any chain of assigned changes, the value of the product of the growing/decreasing factors

<U>DOES NOT DEPEND of their order in the chain</U>.



It provides the answer in this case:  the final growing/decreasing factor is

    (1+0.03)*(1+0.02)*(1+0.01)*(1-0.01)*(1-0.02)*(1-0.03) = 0.9986.



Thus, after the chain of changes, you have finally DECREASE of the price by 

   (1-0.9986)*100 =  0.14%,


<U>I N D E P E N D E N T L Y</U>   of the order of changes in the chain.    


  +----------------------------------------------------------------------------+
  | So, after the given chain of changes, the final price of the stock will be |
  |                                                                            |
  |     10.00 - 0.0014*10.00 = 9.99 cents    (rounded to the closest cent)     |   
  |                                                                            |
  |                                                                            |
  | independently of the order of the pre-assigned changes.     <U>ANSWER</U>         |
  +----------------------------------------------------------------------------+
</pre>

Solved.


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Quite unexpected result, isn't it ?


But a correct one (!)