# Calculating average inflation rate per year

• ainster31
In summary, the conversation discusses an economist's prediction of inflation rates for the next 10 years, with 5 years at 8% and 5 years at 6%. The solution provided is incorrect as it uses an arithmetic average instead of a geometric average. The correct average price change per year is between 6% and 8%. A shortcut for finding the solution is (1+i)^10=1.97 with (1+i)2=1.06*1.08. The textbook authors are Donald G. Newnan, Ted G. Eschenbach, and Jerome P. Lavelle.
ainster31

## Homework Statement

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?

## 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: 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. Yeah, it seems the textbook messed that up too. I've corrected the numbers. ainster31 said: ## Homework Statement 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? ## Homework Equations ## 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.

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

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

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:

Donald G. Newnan is Professor Emeritus of Industrial and Systems Engineering at San Jose State University.

Ted G. Eschenbach is a consultant and Professor Emeritus of Engineering Management at the University of Alaska Anchorage.

Jerome P. Lavelle is Associate Dean in the College of Engineering at North Carolina State University.

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.

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

Chestermiller said:
Try $(1+i)^{10}=1.97$
More simply, (1+i)2 = 1.06*1.08.

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

Ha! Very cute.

Chet

## 1. What is the formula for calculating average inflation rate per year?

The formula for calculating average inflation rate per year is: ((Current year CPI - Previous year CPI) / Previous year CPI) x 100.

## 2. How is the inflation rate measured?

The inflation rate is measured by calculating the percentage change in the Consumer Price Index (CPI) from one year to the next.

## 3. What data is needed to calculate average inflation rate per year?

To calculate average inflation rate per year, you will need the CPI for the current year and the CPI for the previous year.

## 4. Is average inflation rate per year the same as annual inflation rate?

Yes, average inflation rate per year and annual inflation rate refer to the same concept. They both measure the percentage change in CPI over a one-year period.

## 5. How accurate is the calculated average inflation rate per year?

The calculated average inflation rate per year is an approximation and may not reflect the true inflation rate. It is based on the CPI, which is a broad measure of price changes and may not accurately represent the inflation experienced by individual consumers.

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