SOLUTION: Monthly sales figures for January are 5600. This is expected to fall for the following 9 months at a rate of 2% each month. Thereafter sales are predicted to rise at a constant rat

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Question 1149493: Monthly sales figures for January are 5600. This is expected to fall for the following 9 months at a rate of 2% each month. Thereafter sales are predicted to rise at a constant rate of 4% each month. Estimate total sales for the next 2 years (including the first January).
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.

It can be done in 2 ways.


First way is to sum two geometric progressions, using standard formulas.


    First GP starts with 5600 (Jan) and has 9 following terms from 2 to 10 (Feb-Oct) inclusive, 
    that diminish with the common ratio of 0.98.

    Then this term  a%5B10%5D  (Oct)  is the first term of the other, growing GP with the common ratio of 1.04.

    This second sequence continues to the 25-th term a%5B25%5D  inclusive, which corresponds to the last Jan.


          (It is how I understand the problem's description, although it is in fog in this part).


It is really boring way.


Another way is to do it in several clicks with Excel.


I did it in this way and got the ANSWER  148449.09.    ANSWER


Notice that I rounded at the very end and did not round on the way.