Chapter 4.7, Problem 69AYU

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

1. The CPI was to 224.9 for 2011 and 240.0 for 2016. Assuming that annual inflation remained constant for this time period, determine the average annual inflation rate.

2. Using the inflation rate from part (a), in what year will the CPI reach 300?