Chapter 5.7, Problem 72AYU

Problems 69-72 require 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 March 2015 was $236.12$. This means that $\$100$ in the period 1982-1984 had the same purchasing power as $\$236.12$ in March 2015. In general, if the rate of inflation averages $r$ percent per annum over $n$ years, then the CPI index after $n$ years is $CPI=CP{I}_0{\left(1+\frac{r}{100}\right)}^n$ where $CP{I}_0$ is the CPI index at the beginning of the $n\text{-year}$ period.

Source: U.S. Bureau of Labor Statistics

Consumer Price Index The base period for the CPI changed in 1998. Under the previous weight and item structure, the CPI for 1995 was $456.5$. If the average annual inflation rate was $5.57\%$, what year was used as the base period for the CPI?

To determine

To find: Consumer Price Index The base period for the CPI changed in 1998. Under the previous weight and item structure, the CPI for 1995 was $456.5$. If the average annual inflation rate was $5.57\%$, what year was used as the base period for the CPI?

Answer to Problem 72AYU

Solution:

$537.12$

Explanation of Solution

Given:

$CPI=456.5, r=5.57\%$ and $n=3$

Calculation:

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

$CPI = 456.5{\left(1+\frac{5.57}{100}\right)}^3$

$CPI=456.5\left(1.1766\right)$

$CPI=537.12$