this is my problem and i hope you can help me. I need to calculate total inflation for the period 2016-2022 in a certain coutry. The problem is that I can't match the data, obtaining the same result using the consumer price index and the percentages of the annual change. Data:
CPI
2015 ...... 100,0
2016 ...... 99,9
2017 ...... 101,3
2018 ...... 102,5
2019 ...... 103,2
2020 ...... 103,0
2021 ...... 105,0
2022 ...... 114,2
I'm using that formula: (CPI 2022 - CPI 2016) / CPI 2016 x 100. The result is: 14,314%. Is that correct?
Now, I want to obtain the same result only using the annual percentage change (assuming that the consumer price index is not available):
2015 ...... 100,0
2016 ...... 99,9 ...... -0,100%
2017 ...... 101,3 ...... 1,401%
2018 ...... 102,5 ...... 1,185%
2019 ...... 103,2 ...... 0,683%
2020 ...... 103,0 ...... -0,194%
2021 ...... 105,0 ...... 1,942%
2022 ...... 114,2 ...... 8,762%
Trying to do this i'm not obtaining the same result. What is the correct formula? Please, can you show me how to do?
Thanks
Percentages need to be multiplied. Indeed:
$$(1-0.1\%)\cdot(1+1.401\%)\cdots(1+8.762\%)=1.142=1+14.2\%$$