<p>Because inflation is defined as a positive <strong>growth rate of CPI</strong>.</p>
<p>By definition growth rate is:</p>
<p><span class="math-container">$$g=\frac{x_t-x_{t-1}}{x_{t-1}} \tag{*}$$</span></p>
<p>That is just how growth rate is defined in sciences anywhere from physics or biology to social sciences.</p>
<p>It does not matter if the number is in percentages. A growth rate of interest rate is still calculated by the same equation *.</p>
<p><span class="math-container">$x_t-x_{t-1}$</span> is just simple change, not growth rate.</p>
<blockquote>
<p>Assume base year is 2003 and CPI in 2010 was 105% and CPI in 2021 was 120% then should not inflation rate be 120% - 105% = 15%?</p>
</blockquote>
<p>No in that problem CPI changed by 15 points, inflation rate in your example is <span class="math-container">$0.1429$</span> or <span class="math-container">$14.29\%$</span>. Note inflation does not need to be expressed in per cent terms - in many research papers it’s just in decimals.</p>

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2021-12-25T20:51:58.940Z
2021-12-25T20:51:58.940Z
1muflon1
<p>I know that <strong>inflation rate</strong> = <span class="math-container">$$ CPI_{n} - CPI_{n-1} \over  CPI_{n-1}$$</span></p>
<p>but I wonder what's the point of dividing by <span class="math-container">$CPI_{n-1}$</span>, CPI is already a <strong>percentage</strong> so inflation rate should be <span class="math-container">$ CPI_{n} - CPI_{n-1}$</span> directly (eg. Assume base year is 2003 and CPI in 2010 was 105% and CPI in 2021 was 120% then should not inflation rate be 120% - 105% = 15%?)</p>
<p>I suspect we do that because we often tend to think of CPI as in dollars instead of percentage, so for example we can say that what could be bought with 1 dollar in 2003 would be bought with 1.20 dollars in 2021 so we still need to divide by <span class="math-container">$CPI_{n-1}$</span> when calculating inflation rate? but I'm still confused tho.</p>
<p>Thanks in advance (and please ignore how unrealistic my example was, I made that up for demonstration)</p>

<macroeconomics><price-index>
Why do we need to divide by the CPI of year of reference when calculating inflation rate?
AmirWG
# Why do we need to divide by the CPI of year of reference when calculating inflation rate?

(Asked by: username_0 on 2021-12-25)

I know that **inflation rate** = $$ CPI\_{n} - CPI\_{n-1} \over CPI\_{n-1}$$

but I wonder what's the point of dividing by $CPI\_{n-1}$, CPI is already a **percentage** so inflation rate should be $ CPI\_{n} - CPI\_{n-1}$ directly (eg. Assume base year is 2003 and CPI in 2010 was 105% and CPI in 2021 was 120% then should not inflation rate be 120% - 105% = 15%?)

I suspect we do that because we often tend to think of CPI as in dollars instead of percentage, so for example we can say that what could be bought with 1 dollar in 2003 would be bought with 1.20 dollars in 2021 so we still need to divide by $CPI\_{n-1}$ when calculating inflation rate? but I'm still confused tho.

Thanks in advance (and please ignore how unrealistic my example was, I made that up for demonstration)

**Tags:** macroeconomics, price-index

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## 1 answers

### Answer by username_1 on 2021-12-25. Score: 4 | Accepted answer

Because inflation is defined as a positive **growth rate of CPI**.

By definition growth rate is:

$$g=\frac{x\_t-x\_{t-1}}{x\_{t-1}} \tag{\*}$$

That is just how growth rate is defined in sciences anywhere from physics or biology to social sciences.

It does not matter if the number is in percentages. A growth rate of interest rate is still calculated by the same equation \*.

$x\_t-x\_{t-1}$ is just simple change, not growth rate.

> Assume base year is 2003 and CPI in 2010 was 105% and CPI in 2021 was 120% then should not inflation rate be 120% - 105% = 15%?

No in that problem CPI changed by 15 points, inflation rate in your example is $0.1429$ or $14.29\%$. Note inflation does not need to be expressed in per cent terms - in many research papers it’s just in decimals.


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