When we say "inflation has remained steady at 2% for the past 5 years", is that typically taken to mean 2% compounded annually for each of those years, or something else?
When the government and the media report inflation, they are just reporting the annualized rate. If you calculated the compounded value over any length of time it becomes very scary. Also this is why we all have heard stories from older people about normal items costing virtually nothing 40 or 50 years ago.
This article explains the compounding effect pretty well.
It depends on who's providing the statistics. The CPI page on the Bureau of Labor Statistics has a FAQ which discusses this:
... [W]e publish many indexes ... Often, the media will report some, or all, of the following:
- Index level, not seasonally adjusted. (for example, May 2008 = 216.632).
- 12-month percent change, not seasonally adjusted. (for example, May 2007 to May 2008 = 4.2 percent).
- 1-month percent change on a seasonally adjusted basis. (for example, from April 2008 to May 2008 = 0.6 percent).
- Annual rate of percent change so far this year (for example, from December 2007 to May 2008 if the rate of increase over the first 5 months of the year continued for the full year, after the removal of seasonal influences, the rise would be 4.0 percent).
- Annual rate based on the latest seasonally adjusted 1-month change. For example, if the rate from April 2008 to May 2008 continued for a full 12 months, then the rise, compounded, would be 8.1 percent.
A figure like "inflation has been 2% over the past 5 years" probably refers to an annualized rate of increase of 2% a year for the past 5 years, leaving the dollar's purchasing power at about 90% of its original value (or prices at about 110% of their original value).
If you want exact numbers, look up the figures in the index yourself rather than worrying yourself over how to compound an approximation (monthly? yearly? continuously? none of the above!)
Using a compound annual rate as a standard measure makes comparison easier. Trying to compare a X% rise over Y years to a W% rise over Z years requires a bit of math to figure out the equivalency. If everyone lists numbers as an annual rate, a child could tell you which number is bigger without grabbing a calculator. Standards tend to be semi-arbitrary, but they make things easier. Calculating the difference in the buying power of a currency over any significant length of time has little practical purpose (save for idle curiosity and depressing people) compared to analyzing if the inflation rate is too high or low compared to known standards of comparison.
Yes, according to Investopedia:
"Compounding refers to generating earnings [or losses] from previous earnings [or losses]."
This is how inflation works as well.
The graph below clearly shows the compounding effect of inflation.
Inflation must be compounded because there is no "starting" year where money was first given value. When applying 2% interest, this is done to the value of a dollar at its value when the interest was taken. It is also possible to take averages of the inflation rate over a period of years.