Please help,
Just a struggling student here -- If I know inflation between year one and year two, and between year two and year three, and so on -- How do I calculate the average annual inflation over a multi-year period -- There has to be a formula which involves plugging in the annual inflation rate for each and every year --
Thanks in advance.
No - you just have to convert the percentages it values to find the ending index value. If you don't have a start value use any number - I've used 100 -
eg
Year 1 inflation = 3.5% Year 2 inflation = 2.0% Year 3 inflation = 2.5%
You need to convert it into an index (or use the government RPI index values) to find the final value -
Year 0 = 100 Year 1 = Previous figure x (1 + (3.5 / 100)) = 103.5 Year 2 = Previous figure x (1 + (2.0 / 100)) = 105.57 Year 3 = Previous figure x (1 + (2.5 / 100)) = 108.20925
This shows that inflation has been 8.20925% over 3 years. Then take the original (100) and final value (108.20925) and put them through the reverse cumulation formula -
(((((OriginalValue+GainOrLoss)/OriginalValue)^(1/Duration))-1)*100
(((((100+8.20925) / 100) ^ (1 / 3)) - 1) * 100
=2.66477561 average inflation during the 3 years
You can double check this by running the cumulation formula to turn it back into an index value -
100 * ((2.66477561 / 100 + 1) ^ 3) = 108.20925 ie 8.20925% higher than the starting value of 100 after 3 years.hth
Daytona
Easy. Convert each inflation rate to a factor, so 3.5% becomes 1.035,
2.3% becomes 1.023, and so on. Multiply all N factors together and then take the Nth root of the product. Then convert the factor so obtained back to a percentage in the obvious way.Daytona has the right idea but needs lessons in how to be concise. :-)
Nah - just testing :-))
In message , Ronald Raygun writes
Hmmm, how times move one.............................. :-)
The words "black", "pot" and "kettle" spring to mind :)
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