# WHAT IS THE AVERAGE INFLATION RATE IF IT GOES FROM 5% TO 4% AND THEN TO 6%?

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If these inflation rates that you give are rates for each period (like a year or a quarter) then the average rate for those three periods is 5%.

If that's what you are asking, you just figure it out like you would figure any kind of an average. You take the three numbers and add them together. That gets you 15 in this case. Then you divide it by the number of periods you are talking about. That's three in this case.

So 15/3 = 5.

So the average rate of inflation over those three years would be 5%.

The answer given above are true only if we do not consider the base figure over which the average inflation rate is calculated. But if we consider the change in base rates over three years then the average inflation rate will be different. To understand why, let us look at the following figures.

Let us average that the price index at the beginning of a year was 100. A 5% inflation will increase this price index to 105 at the beginning of the second year. A 4% increase in this index of 105 will be calculated as:

Price index at end of 2nd year

= Price index at beginning of 2nd year)*(100 + percentage rise)/100

= 105*(100 + 4)/100 = 105*1.04 = 109.2

Similarly Price index at the end of 3rd year

= Price index at beginning of 2nd year)*(100 + percentage rise)/100

= 109.2*(100 + 6)/100 = 109.2*1.06 = 115.752

Thus the total increase in price index in three years is 15.752%. This works out to simple average annual increase

= 15.752/3 = 5.25067%

If we want to calculate the compound rate of increase it will be

= [(115.752/100)^(1/3) - 1]8100

= 4.995%

The computation of the inflation is based on index numbers.

If y is the index number in the current year and x is the index number in the base year, then inflation in present over the base year is [(y-x)/x]100%.

If 105 , 104 and 106 are the index numbers during 3 periods compared compared to the base year index number at 100, then

the average index number for the period is (105+104 + 106)/3 =105. So the inflation rate is [105-100)/100]100 = 5%.