1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    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

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

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

    Chet
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Calculating average inflation rate per year
  1. Average Rate Problem (Replies: 2)

  2. Inflation Rate Problem (Replies: 6)

Loading...