The consumer price index, or cpi, has the following formula:
\(CPI = \frac{Current \ Period \ Price}{Base \ Period \ Price} \ x \ 100\)
Let's compute the real base period price for the cpi today.
\(120 = \frac{11}{Base \ Period \ Price} \ x \ 100\)
Base Period Price = $9.2
Then, we compare the apparent with the real:
Real Base Period: $11 - $9.2 = $1.8
Apparent Base Period: $11 - $10 = $1
Real > Apparent, thus your real wage rate has increased since 2005.