If inflation had been 3% each year from 2005 to 2015, what would the CPI have been in 2015?
To calculate the Consumer Price Index (CPI) in 2015 based on an assumed inflation rate of 3% per year from 2005 to 2014, follow these steps:
Step 1: Determine the base year
The base year is the initial reference point for calculating the CPI. In this case, the base year is 2005.
Step 2: Calculate the cumulative inflation rate
To find the cumulative inflation rate from 2005 to 2014, sum up the individual inflation rates for each year. Since the assumed inflation rate is 3% per year, the cumulative inflation rate can be calculated as follows:
Cumulative Inflation Rate = (1 + Inflation Rate1) x (1 + Inflation Rate2) x ... x (1 + Inflation Rate n) - 1
In our case, n = 9 (2005 to 2014):
Cumulative Inflation Rate = (1 + 0.03)^(2014-2005) - 1
= (1 + 0.03)^9 - 1
= 1.2950 - 1
= 0.2950
So, the cumulative inflation rate from 2005 to 2014 is 0.2950 or 29.50%.
Step 3: Calculate the CPI in 2015
The formula for calculating the CPI in a given year (Let's call it CPIx) is:
CPIx = CPIbase year x (1 + Cumulative Inflation Rate)
For our calculation, CPIbase year is the CPI in the base year (2005). Let's assume it is 100.
CPI2015 = CPI2005 x (1 + 0.2950)
= 100 x (1 + 0.2950)
= 100 x 1.2950
= 129.50
Therefore, if the inflation rate remained at 3% per year from 2005 to 2014, the CPI in 2015 would have been approximately 129.50.