# Calculate average annual inflation

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?

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: $$2012 -1993 = 19 \Rightarrow s=19$$

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

• 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
Sep 8 '21 at 11:19