# Calculating average inflation rate per year

1. Feb 19, 2014

### ainster31

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. Feb 19, 2014

### SteamKing

Staff Emeritus
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.

3. Feb 19, 2014

### ainster31

Yeah, it seems the textbook messed that up too. I've corrected the numbers.

4. Feb 19, 2014

### Ray Vickson

Why are you using an 'arithmetic' average (0.97/10) in a problem having 'geometric' growth?

5. Feb 19, 2014

### ainster31

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:

6. Feb 19, 2014

### haruspex

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.

7. Feb 19, 2014

### Staff: Mentor

Try $(1+i)^{10}=1.97$

8. Feb 20, 2014

### haruspex

More simply, (1+i)2 = 1.06*1.08.

9. Feb 20, 2014

### Staff: Mentor

Ha! Very cute.

Chet