<p>The calculation goes like:</p>
<p>Price index @ 1993 =  60 <span class="math-container">$ \Rightarrow X_{t+s}=0.6  $</span></p>
<p>Price index @ 2012 = 100 <span class="math-container">$ \Rightarrow X_{t}=1$</span></p>
<p>Number of years from 1993 to 2012: <span class="math-container">$ 2012 -1993 = 19 \Rightarrow s=19$</span></p>
<p><span class="math-container">$100*((\frac{X_{t+s}}{X_t})^{(\frac{1}{s})}-1) = 100*(\frac{1}{0.6} ^{(1/19)}-1)=100*(\sqrt[19]{(5/3)}-1)=2.72502$</span></p>

CC BY-SA 4.0
2021-09-08T11:19:04.460Z
You may want to add that you use the *geometric average* here, because the price levels is obtained by compounding of the inflation rates over time.
BrsG
CC BY-SA 4.0
2021-03-04T16:42:43.420Z
2021-08-08T20:33:20.087Z
2021-08-08T20:33:20.087Z
done
<p>The price index in the year 1993 is 60.</p>
<p>The base at 2012 is 100.</p>
<p>The annual nominal interest rate between 1993 and 2012 is 66% on average.</p>
<p>What is the average annual inflation between 1993 and 2012?</p>
<p>I know that</p>
<p>Inflation = <span class="math-container">$\frac{X_{t+s}-X_t}{X_t}$</span>x<span class="math-container">$ 100$</span></p>
<p>where <span class="math-container">$X_{t+s}$</span> is the current year and <span class="math-container">$X_t$</span> is the year being compared.</p>
<p>However, when I use this formula with <span class="math-container">$X_{t+s}=100$</span> (since it is the base of the index) and <span class="math-container">$X_t=60$</span>, I just get the annual nominal interest rate of 66.6666%.</p>
<p>What did I do wrong here?</p>

<macroeconomics><mathematical-economics><inflation><nonexpert>
Calculate average annual inflation
Econ student
# Calculate average annual inflation

(Asked by: username_0 on 2021-03-02)

The price index in the year 1993 is 60.

The base at 2012 is 100.

The annual nominal interest rate between 1993 and 2012 is 66% on average.

What is the average annual inflation between 1993 and 2012?

I know that

Inflation = $\frac{X\_{t+s}-X\_t}{X\_t}$x$ 100$

where $X\_{t+s}$ is the current year and $X\_t$ is the year being compared.

However, when I use this formula with $X\_{t+s}=100$ (since it is the base of the index) and $X\_t=60$, I just get the annual nominal interest rate of 66.6666%.

What did I do wrong here?

**Tags:** macroeconomics, mathematical-economics, inflation, nonexpert

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## 1 answers

### Answer by username_1 on 2021-03-04. Score: 1

The calculation goes like:

Price index @ 1993 = 60 $ \Rightarrow X\_{t+s}=0.6 $

Price index @ 2012 = 100 $ \Rightarrow X\_{t}=1$

Number of years from 1993 to 2012: $ 2012 -1993 = 19 \Rightarrow s=19$

$100\*((\frac{X\_{t+s}}{X\_t})^{(\frac{1}{s})}-1) = 100\*(\frac{1}{0.6} ^{(1/19)}-1)=100\*(\sqrt[19]{(5/3)}-1)=2.72502$

> **Comments:**
> **username_2**: You may want to add that you use the *geometric average* here, because the price levels is obtained by compounding of the inflation rates over time.  

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