Your definition of "actual price" is different than what it should be. The CPI should show an average of what the populace is currently paying for rent. That is

Your definition of "actual price" is different than what it should be. The CPI should show an average of what the populace is currently paying for rent. That is to say some people are locked into a low rate from years ago. Some people are locked into a slightly higher rate from a year to just a few months ago. Still others are paying market rates if they just negotiated their prices recently. CPI does not and should not show only what those paying the current rates are paying. It should show an average of what the entire population is paying.