Chapter 5.7, Problem 70AYU

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 If the current CPI is $234.2$ and the average annual inflation rate is $2.8\%$, what will be the CPI in 5 years?

To determine

To find: Consumer Price Index If the current CPI is $234.2$ and the average annual inflation rate is $2.8\%$, what will be the CPI in 5 years?

Answer to Problem 70AYU

Solution:

$CPI=268.87$

Explanation of Solution

Given:

$CP{I}_0=234.2, r=2.8\%$ and $n=5$

Calculation:

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

$= 234.2{\left(1+\frac{2.8}{100}\right)}^5$

$=268.87$

CPI after 5 years is $268.87$.