The Consumer Price Index (CPI) indicates the relative change...

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 CPluses the base period $1982-1984$ for comparison (the CPIfor this period is 100 . The CPI for Jamuary 2006 was I98.3. This means that sioo in the period $1982-1984$ had the same purchasing power as $\$ 198.30$ in Jamuary 2006 . In general, if the rate of inflation averages r per anmum over n years, then the CPIindex after n years is $$\mathrm{CPI}=\mathrm{CPI}_{0}\left(1+\frac{r}{100}\right)^{n}$$ where $C P I_{0}$ is the CPI index at the beginning of the $n$ -year period. (a) The CPI was 163.0 for 1998 and 215.3 for $2008 .$ Assuming that annual inflation remained constant for this time period, determine the average annual inflation rate. (b) Using the inflation rate from part (a), in what year will the CPI reach $300 ?$

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 CPluses the base period $1982-1984$ for comparison (the CPIfor this period is 100 . The CPI for Jamuary 2006 was I98.3. This means that sioo in the period $1982-1984$ had the same purchasing power as $\$ 198.30$ in Jamuary 2006 . In general, if the rate of inflation averages r per anmum over n years, then the CPIindex after n years is $$\mathrm{CPI}=\mathrm{CPI}_{0}\left(1+\frac{r}{100}\right)^{n}$$ where $C P I_{0}$ is the CPI index at the beginning of the $n$ -year period.
(a) The CPI was 163.0 for 1998 and 215.3 for $2008 .$ Assuming that annual inflation remained constant for this time period, determine the average annual inflation rate.
(b) Using the inflation rate from part (a), in what year will the CPI reach $300 ?$

Key Concepts

Consumer Price Index

The Consumer Price Index (CPI) is an economic indicator that tracks the average change in prices over time for a fixed basket of goods and services. It provides insight into the cost of living and is commonly used to gauge inflation, allowing comparisons of purchasing power between different time periods.

Inflation Rate

The inflation rate is the percentage change in the general price level of goods and services in an economy over a given period. It indicates how quickly prices are rising, affecting the real value of money, and is essential for making economic forecasts and policy decisions.

Compound Growth

Compound growth refers to the process where growth in the value of an asset or index accumulates over time at a constant rate. In the context of price indices and inflation, it involves applying a consistent annual inflation rate to compute the cumulative effect over multiple years using an exponential formula.

Base Period

A base period is a selected time span used as a benchmark against which later price changes are measured. By setting a specific value for the CPI during this period, it becomes easier to compare changes in the cost of living over time and evaluate the impact of inflation.

Exponential Forecasting Model

The exponential forecasting model is a mathematical approach used to predict future values by applying a constant percentage change to the current value over successive periods. This model is particularly useful in understanding how inflation can compound over time to affect the Consumer Price Index.

Transcript

00:01 Okay, this problem is a consumer price index problem, and they give you a really nice formula, so we'll just start right there.

00:08 The consumer price index equals the consumer price index.

00:14 Sub -zero means the initial amount.

00:16 It is the beginning consumer price index for the n year period.

00:21 So that is where we're going to begin, and then we'll finish up one plus r over 100.

00:27 R is whatever rate they're talking about, and n is the time in years.

00:31 Well, if you read the problem, it says the cpi was 163 for 1998.

00:36 Well, that's where you're beginning, so 163 .0 is that.

00:41 They continue telling us that the cpi in 2008 is 215 .3, and if you notice, the distance, excuse me, the time that is elapsed from 2008 to 1998 is 10 years, so that is your n, and it is the r in this problem that you are solving for because they want to know the average annual inflation rate, so r, of course, is the rate.

01:15 Excuse me.

01:17 So i will, excuse me again.

01:22 So i will need to divide each side by 163 in order to begin to isolate that r.

01:34 So 215 .3 divided by 163 is some version of 1 .32 .3.

01:42 So i'm gonna do 0 .2086, and you can get a very nice, well, a more exact answer on your calculator.

01:52 I have the wrong number up here.

01:54 I should erase that.

01:55 That's just a 10.

01:56 That's my mistake...