lesson

Calculating an Inflation Rate

After you have worked through this section of the learning unit, you should be able to calculate, using the CPI, inflation rates based on

month on same month of previous year
annual average on annual average
month on previous month at an annual rate
quarterly average on previous quarterly average at an annual rate

Start Activities

Print Page

Study Instructions

Study chapter 6.4 of the textbook.

Do the activities.

Introduction

1 Complete the following table by calculating the inflation rate on month on same month of previous year:

Month 2019	Inflation rate (%)
January
February
March
April
May
June
July
August
September
October
November
December

Month 2019	Inflation rate (%)
January	4,0
February	4,1
March	4,5
April	4,4
May	4,5
June	4,5
July	4,3
August	4,1
September	4,1
October	3,7
November	3,6
December	4,0

The calculation for March 2019 is as follows:

$$
\Biggl[
\Biggl(
\frac{\text{CPI March 2019}}{\text{CPI March 2018}}
\Biggl)-1
\Biggl]
\times 100
$$

$$
\Biggl[
\Biggl(
\frac{\text{110,0}}{\text{106,2}}
\Biggl)-1
\Biggl]
\times 100
$$

= (1,045 -1) X 100
= 4,5%

[Insert video clip]

2 Based on a month on same month of previous year calculation, the inflation rate decelerated (disinflation) from 4,5% in March 2019 to 4,0% in December 2019.

True

Correct. The statement is indeed true.

Month 2019	Inflation rate (%)
January	4,0
February	4,1
March	4,5
April	4,4
May	4,5
June	4,5
July	4,3
August	4,1
September	4,1
October	3,7
November	3,6
December	4,0

False

Incorrect. The statement is true.

Month 2019	Inflation rate (%)
January	4,0
February	4,1
March	4,5
April	4,4
May	4,5
June	4,5
July	4,3
August	4,1
September	4,1
October	3,7
November	3,6
December	4,0

4 An increase in value-added tax (VAT) on 1 April 2018 from 14% to 15% could have created statistical noise in the data.

True

Correct. The statement is indeed true.

The inflation rates calculated according to month on same month of previous year are subject to wide fluctuations. This can be due to statistical noise which might be the result of something such as an increase in VAT. Another factor that contributes to statistical noise is that not all prices are measured every month and the base effect – what happened one year ago – has as much effect as what happened in the latest period.

False

Incorrect. The statement is true.

7 The inflation rate (annual average on annual average) for 2019 is …

Correct. The inflation rate is 4,1%.

The calculation is as follows:

$$
\Biggl[
\Biggl(
\frac{\text{Average CPI for 2019}}{\text{Average CPI for 2018}}
\Biggl)-1
\Biggl]
\times 100
$$

$$
\Biggl[
\Biggl(
\frac{\text{112,2}}{\text{107,8}}
\Biggl)-1
\Biggl]
\times 100
$$

= (1,041 -1) x 100
= 4,1%

Incorrect. The inflation rate is 4,1%.

The calculation is as follows:

$$
\Biggl[
\Biggl(
\frac{\text{Average CPI for 2019}}{\text{Average CPI for 2018}}
\Biggl)-1
\Biggl]
\times 100
$$

$$
\Biggl[
\Biggl(
\frac{\text{112,2}}{\text{107,8}}
\Biggl)-1
\Biggl]
\times 100
$$

= (1,041 -1) x 100
= 4,1%

8 Calculating the inflation rate using the annual average CPI on annual average CPI gives a good indication of short-term changes in the inflation rate.

True

Incorrect. The statement is false.

This method has to be supplemented by other methods such as the comparison of month to the same month of the previous year and month on previous month at an annual rate.

The annual average CPI on annual average CPI gives a better indication of the intensity of the inflation process over a longer period.

False

Correct. The statement is indeed false.

This method has to be supplemented by other methods such as the comparison of month to the same month of the previous year and month on previous month at an annual rate.

The annual average CPI on annual average CPI gives a better indication of the intensity of the inflation process over a longer period.

9 Use the online statistical tool of the South African Reserve Bank to find the data for the monthly seasonally adjusted CPI (KBP7170N) and calculate the inflation rate using month on previous month at an annual rate.

Tool: online statistical tool

Period	CPI monthly seasonally adjusted	Inflation rate (%)
2018/12
2019/01
2019/02
2019/03
2019/04
2019/05
2019/06
2019/07
2019/08
2019/09
2019/10
2019/11
2019/12

Period	CPI monthly seasonally adjusted	Inflation rate (%)
2018/12	109.3	-
2019/01	109.2	-1,1
2019/02	109.5	3,3
2019/03	110.1	6,8
2019/04	110.8	7,9
2019/05	111.2	4,4
2019/06	111.7	5,5
2019/07	111.7	0,0
2019/08	112.5	8,9
2019/09	112.8	3,2
2019/10	112.8	0,0
2019/11	113.3	5,5
2019/12	113.6	3,2

The calculation for December 2019 is

$$
\Biggl[
\Biggl(
\frac{113,6}{113,3}
\Biggl)^\text{12} -1
\Biggl]
\times 100
$$

= (1,003¹²– 1) x 100
= 1,023 -1) x 100
= 0,032 x 100
= 3,2%

10 South Africa’s Covid-19 lockdown began on 26 March 2020. For the whole of April 2020 the country was on a lockdown level 5. Based on month on same month of previous year, the inflation rate for March 2020 was 4,1%. For April 2020, based on month on same month of previous year, the inflation rate was 3%. Using seasonally unadjusted data for CPI, the percentage increase from March 2020 to April 2020 was –0,5%. Using seasonally adjusted data for CPI, the inflation rate month on previous month at an annual rate is …

(Still wait for the data to be published)

11 The inflation data for month on previous month shows very little variation.

True

Incorrect. The statement is false.

The inflation rate based on monthly changes shows a significant degree of variation. For instance, the inflation rate for August 2019 was 8,9%, whereas for October 2019 it was 0,0%.

False

Correct. The statement is indeed false.

The inflation rate based on monthly changes shows a significant degree of variation. For instance, the inflation rate for August 2019 was 8,9%, whereas for October 2019 it was 0,0%.

12 Use the following data to calculate the inflation rate for the last quarter of 2019 using quarterly average on previous quarterly average at an annualised rate:

Time period	CPI (seasonally adjusted)
2019/07	111,7
2019/08	112,5
2019/09	112,8
2019/10	112,8
2019/11	113,3
2019/12	113,6

The inflation rate (one decimal point) for the last quarter of 2019 was …

Correct. The inflation rate for the last quarter of 2019 was 3,2%.

The average for the third quarter was (111,7 + 112,5 + 112.8)/3 = 112,3
The average of the last (fourth) quarter was (112,8 + 113,3 + 113,6)/3 = 113,2

The inflation rate was

$$
\Biggl[
\Biggl(
\frac{113,2}{112,3}
\Biggl)^4 -1
\Biggl]
\times 100
$$

= (1,008⁴– 1) x 100
= (1,032 -1) x 100
= 0,032 x 100
= 3,2%

Incorrect. The inflation rate for the last quarter of 2019 was 3,2%.

The average for the third quarter was (111,7 + 112,5 + 112.8)/3 = 112,3
The average of the last (fourth) quarter was (112,8 + 113,3 + 113,6)/3 = 113,2

The inflation rate was

$$
\Biggl[
\Biggl(
\frac{113,2}{112,3}
\Biggl)^4 -1
\Biggl]
\times 100
$$

= (1,008⁴– 1) x 100
= (1,032 -1) x 100
= 0,032 x 100
= 3,2%

Concepts

Average annual inflation rate

The change in the average index of one year compared with the average index of the previous year, expressed as a percentage.
Annual percentage change

The change in the index of the relevant month of the current year compared with the index of the same month in the previous year, expressed as a percentage.
Annual inflation rate

The change in the index of the relevant month of the current year compared with the index of the same month in the previous year, expressed as a percentage.
Annualised rate

A rate of change for a given period that is less than a year, but it is calculated as if the rate were for a full year.

Glossary

lesson

Calculating an Inflation Rate

Study Instructions

Introduction