*** sorry for double question *** Please, i'm going crazy :) 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 annual percentage 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%
I have tried to multiplicate percentages but doing this the result is 14.2%. Doing other examples the gap seems relevant.
Also consider this case (same years 2016-2022)
LCI - Labour cost index
2015 ...... 92,7
2016 ......92,3
2017 ......93,1
2018 ......94,9
2019 ......96,4
2020 ......100,0
2021 ......99,3
2022 ......101,9
Percentages:
2015 ......92,7
2016 ......92,3...... -0,431%
2017 ......93,1...... 0,867%
2018 ......94,9...... 1,933%
2019 ......96,4 ...... 1,581%
2020 ......100,0 ...... 3,734%
2021 ......99,3 ...... -0,700%
2022 ......101,9..... 2,618%
Result using LCI: 10,401%
Result using percentages multipliation : 9,54%
Is that right? Why?
Thanks
Starting at $99.9$ in 2016, eventually we landed at $114.2$ in 2022. Therefore, the currency inflated $\frac{114.2 - 99.9}{99.9} = 143/999 \approx 14.3\%$ from 2016 to 2022.