Between 2005 and 2009 the average rate of inflation was about 2.2% per year. if a cart of groceries cost $120 in 2005, what did it cost in 2009?

In the problem it is already given that the average rate of inflation per year between 2005 and 2009 is 2.2%. the price of the product in 2005 is $120. It is required to find the rate of the product in the year 2009.
In the year 2006 rate of increase of the product price = 120 * (2.2/100) dollars
                                                                            = 2.64
Then price in 2006 = (120 +2.64) dollars
                              = 122.64 dollars
In the year 2007 rate of increase of the product price = 122.64 * (2.2/100) dollars
                                                                                     = 2.69 dollars
Then price in 2007 = 125.34 dollars
In the year 2008 rate of increase of the product price = 125.34 * (2.2/100)
                                                                                     = 2.75 dollars
Then price in 2008 = 128.09
In the year 2009 rate of increase of the product price = 128.09 * (2.2/100) dollars
                                                                                     = 2.82 dollars
Then the price in 2009 = 130.91
In the year 2009 the product cost $130.91