# Suppose the CPI was 110 last year and is 121 this year.

– Part-(a) Calculate the rate of inflation this year in terms of percentage. Express the answer in the form of a whole number in Part-(a).

– Part-(b) In contrast to Part-(a), calculate the rate of inflation this year if the CPI is supposed to be $110$ for last year and $108$ for this year. Express the answer by rounding off to 1 decimal place.

– Part-(c) Explain the terminology which is used by the economists to describe the answer to Part-(b) (Inflation or Deflation)

The aim of this question is to find the rate of inflation by comparing the CPI of this year with the CPI of last year.

The basic concept behind this article is the calculation of the rate of increase or decrease also known as Percentage Increase or Decrease. Increase or decrease is expressed in terms of positive or negative value respectively.

For the Percentage Increase/Decrease calculation between two values, we use the following formula:

$Percentage\ Increase/Decrease=\frac{Final\ Value-Initial\ Value}{Initial\ Value}\times 100$

CPI is the abbreviation for Consumer Price Index which is used to track the rate of inflation by observing the changes in the cost of living over time.

Part-(a)

Given that:

This Year’s CPI $=121$

Last Year’s CPI $=110$

The Rate of Inflation is calculated as follows by using the Percentage Increase or Decrease Formula:

$Rate\ of\ Inflation=\frac{This\ Year\ CPI-Last\ year\ CPI}{Last\ year\ CPI}\times 100$

Substituting the given values:

$Rate\ of\ Inflation=\frac{121-110}{110}\times 100$

$Rate\ of\ Inflation=\frac{11}{110}\times 100$

$Rate\ of\ Inflation=0.1\times 100$

$Rate\ of\ Inflation=10\%$

The answer shows a positive rate of inflation which means that the inflation this year is increasing as compared to last year.

Part-(b)

Given that:

This Year’s CPI $=108$

Last Year’s CPI $=110$

The Rate of Inflation is calculated as follows by using the Percentage Increase or Decrease Formula:

$Rate\ of\ Inflation=\frac{This\ Year\ CPI-Last\ year\ CPI}{Last\ year\ CPI}\times 100$

Substituting the given values:

$Rate\ of\ Inflation=\frac{108-110}{110}\times 100$

$Rate\ of\ Inflation=\frac{-2}{10}\times 100$

$Rate\ of\ Inflation=-0.0181\times 100$

$Rate\ of\ Inflation=-1.81\%$

To express the answer with 1 decimal place:

$Rate\ of\ Inflation=-1.8\%$

The answer shows a negative rate of inflation, which means that the inflation this year is decreasing as compared to last year.

Part-(c)

The negative rate of inflation means that the rate of inflation is decreasing as compared to last year.

A negative rate of inflation is expressed as Deflation by Economists, hence the answer of Part-(b) represents Deflation.

## Numerical Result

Part-(a) The Rate of Inflation is $10\%$, which means that the inflation this year is increasing as compared to last year.

Part-(b) The Rate of Inflation is $-1.8\%$, which means that the inflation this year is decreasing as compared to last year.

Part-(c)

The answer of Part-(b) represents the Negative rate of inflation, which is expressed as Deflation by the Economist.

## Example

The current price of a car is $USD-8000$. It was $USD-6500$ last year. Calculate the rate of increase in the car price.

Solution

The Rate of Increase is calculated as follows:

$Rate\ of\ Increase=\frac{This\ Year\ Car\ Price-Last\ year\ Car\ Price}{Last\ year\ Car\ Price}\times 100$

$Rate\ of\ Increase=\frac{8000-6500}{6500}\times 100$

$Rate\ of\ Increase=0.2307\times 100$

$Rate\ of\ Increase=23.07\%$