Chapter 4.7, Problem 71AYU

Problems 69 – 72 require the following discussion. The consumer price index(CPI) indicates the relative change in the 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 1982-84 for comparison (the CPI for this period is 100). The CPI for March 2017 was $243.80. This means that $100 in the period 1982-84 has the same purchasing power as $243.80 in March 2017. In general, if the rate of inflation averages r percent per annum over n years, then CPI index after n years is

$CPI=CP{I}_0{\left(1+\frac{r}{100}\right)}^n$

Where, CPI₀ is the CPI index at the beginning of the n-year period

Consumer Price Index 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.)