Calculate average annual inflation

Question

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?

Answer 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$

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