If the average annual inflation rate is 3.1%, how long will it take for the CPI index to double? (A doubling of the CPI index means purchasing power is cut in half.)

Problem requires the following discussion. The Consumer Price Index (CPI) indicates the relative change in price over time for a fixed basket of goods and services. It is a cost of living index that helps measure the effect of inflation on the cost of goods and services. The CPI uses the base period 1982???1984 for comparison (the CPI for this period is 100). The CPI for January 2006 was 198.3. This means that $100 in the period 1982???1984 had the same purchasing power as $198.30 in January 2006. In general, if the rate of inflation averages r per annum over n years, then the CPI index after n years is

where CPI₀ is the CPI index at the beginning of the n-year period.

CPIO 1 + 100 CPI