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Homework Help: Calculating average inflation rate per year

  1. Feb 19, 2014 #1
    1. The problem statement, all variables and given/known data

    An economist has predicted that for the next 5 years, annual inflation will be 8%, and then there will be 5 years at a 6% inflation rate. This is equivalent to what average price change per year for the entire 10-year period?

    2. Relevant equations

    3. The attempt at a solution

    This is the solution given:

    To buy $1 worth of goods today will require:
    F = P (F/P, f%, n) n years hence.
    F = $1 (1 + 0.08)5 = $1.47 5 years hence.

    For the subsequent 5 years the amount required will increase to:
    $1.47 (F/P, f%, n) = $1.47 (1 + 0.06)5 = $1.97

    Thus for the ten year period $1 must be increased to $1.97. The average price change per year is:
    ($1.97 - $1.00)/10 yrs = 9.7% per year

    Isn't this wrong? You can't just divide the average price change per year because it compounds, right?

    I've tried verifying the answer and it appears wrong to me:

    $$F=$1(1+0.097)^{ 10 }\\ F=$2.52$$

    which is not equal to the $1.97 we were expecting.
    Last edited: Feb 19, 2014
  2. jcsd
  3. Feb 19, 2014 #2


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    The OP states that the inflation rate is 8% for the first 5 years, and then the rate drops to 6% for the next 5 years. These were not the numbers used in your calculations.
  4. Feb 19, 2014 #3
    Yeah, it seems the textbook messed that up too. I've corrected the numbers.
  5. Feb 19, 2014 #4

    Ray Vickson

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    Why are you using an 'arithmetic' average (0.97/10) in a problem having 'geometric' growth?
  6. Feb 19, 2014 #5
    Yeah, this textbook is terrible. It has way too many errors. I'm not sure how high these authors were when they wrote this textbook:

  7. Feb 19, 2014 #6


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    Yes, it's quite obvious that the answer must be between 6% and 8%. In fact, because the two periods are the same there's a very easy shortcut.
  8. Feb 19, 2014 #7
    Try [itex](1+i)^{10}=1.97[/itex]
  9. Feb 20, 2014 #8


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    More simply, (1+i)2 = 1.06*1.08.
  10. Feb 20, 2014 #9
    Ha! Very cute.

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