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%
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