# Methods of calculating 12 month Inflation rates

I was trying to understand inflation calculations when i came across this Scenario, they are trying to calculating the 12 month inflation rate , but the weighted figures given(essentially percentage multipliers ), both have a base year of 2002 .

So when trying to calculate the 12 month inflation rate over that period they found the percentage change between the two weighted figured ,while this is correct ,mathematically i dont understand how this works as in this isnt something that would intuitively come to me and i still dont logically understand why this actually works and shows the percentage change in between in actuall prices between these 2 points in time .

If someone could layout a step by step mathematical working out, as to why this make sense , id be grateful as im really trying to visualise what happens to "proportionality" here for this method to work ,as i completely lost track.

When creating any index the base year is just year of which quantity is used to divide all other quantities. Hence general formula for index number for a random observation $$X_i$$ with base $$n$$ is simply:

$$Index = \frac{X_i}{X_n}$$

This sort of transformation preserves the rates of change since:

$$\frac{\frac{X_t}{X_n}- \frac{X_{t-1}}{X_n}}{\frac{X_t}{X_n}} = \frac{X_t- X_{t-1}}{X_t}$$