Topic Workbook - Basic Mathematics

1 Basic Mathematics 1 Chapter overview An understanding of basic mathematics is essential not only for accounting and finance but also for many situations related to personal finance such as taking out loans, making bank deposits and calculating repayments for items bought on credit etc. This topic will cover percentages and various types of calculations related to percentages. The knowledge here will be useful for the other topics on inflation and interest rates when performing calculations. 1 Learning outcomes By the end of this topic you should be able to: • Solve percentage of a number as well as percentage increases and decreases • Solve problems related to inflation using both the retail price index and consumer price index • Solve problems related to compound interest and also use the geometric mean to calculate interest rates During this topic you will develop your understanding of these concepts and also strengthen your ability to perform related calculations. 1 Chapter summary In this topic, we will cover one of the most fundamental type of calculations you need to be comfortable with when studying and working in the field of accounting and finance – percentages. Having an understanding of and being able to perform calculations related to percentages will also be useful in day-to-day transactions; from calculating revised prices after percentage increases or decreases on products and services to calculating interest on loans and understanding inflation. Regarding inflation, we will look at why inflation occurs, measures of inflation and also briefly look at the concept and impacts of hyperinflation. The final aspect of this chapter will look at interest, including compound interest. We will use the future value formula to calculate the future value of an investment where interest is compounded. We will also see how the geometric mean can be used to calculate interest rates. 1 Key takeaways • Calculations that can be performed with percentages include calculating the percentage of a number, calculating percentage increases and decreases and calculating missing values. • Inflation refers to the increase in prices and can be caused by reasons including excess demand or shortage of supply • Interest rates reflect the opportunity cost of borrowing or depositing money

• Compound interest is ‘interest on interest’ and has the potential to drastically increase the value of an investment as well as increase the amount to be paid on a loan 2 Paper title

1 Context 1.1 Where is Mathematics in everyday life? Everywhere! Mathematics is used in all fields, from engineering and architecture to business and finance, and even in art! It is also important to have a good grasp of basic mathematics for personal finance reasons to ensure the best deals on financial products such as loans and deposits, as well as to understand fundamental economic indicators such as interest rates set by the central bank as well as inflation rates. 1.2 Why is basic Mathematics important for Accounting and Finance? Although you can understand most of the accounting and finance discipline without any complex mathematics, you must have a solid grasp of basic mathematics in order to understand and navigate your way through this field. One of the most fundamental areas is percentages. Although most people can calculate a percentage of a number, performance may be mixed when it comes to calculating percentage increase and decrease and finding missing values. Once your basic understanding is solid, you can build on this to perform calculations related to interest, inflation and a whole host of other areas of calculations involving percentages. 2 Percentages Percentages are everywhere, from calculating money saved on discounted products to calculating interest rates on loans. Here we examine different types of calculations related to percentages. 2.1 What is a percentage? Percentage: A percentage is a proportion that shows a number as parts per hundred. The KEY symbol ‘%’ means ‘per cent’. TERM 9% means 9 out of every 100, or 9/100. Percentages are just one way of expressing numbers that are part of a whole. These numbers can also be written as fractions or decimals. 50% can also be written as a fraction, 1/2, or a decimal, 0.5. They are all exactly the same amount. Knowledge of converting between decimals, fractions and percentages is required (BBC, 2020). 2.2 Fractions, proportions and percentages These three terms seem to differ considerably, but actually fractions, proportions and percentages are merely contrasting ways to express one part of an amount relative to the whole. For instance, suppose a company employs 100 people of whom 25 are women, we could express this as: • women make up one-quarter of the labour force, or • women make up 0.25 of the labour force, or • women make up 25% of the labour force. In this list, the quarter is the fraction, 0.25 is the proportion and 25% is the percentage. Each of these has the same meaning as four quarters make a total of one, four times 0.25 is one and four times 25% is 100%. Note that all of them are numbers smaller than 1, including 25%, which at first sight seems larger than one. To avoid any confusion over this remember that %, per cent, means per hundred, so 25% is actually 25/100 (Buglear 2012, p.12). 2.3 How to calculate the percentage of a number Percentages of amounts can be calculated by writing the percentage as a fraction or decimal and then multiplying it by the amount in question. 1: Basic Mathematics 3

Illustration 1: Calculating the percentage of a number 1 Find 16% of 40. 2 This example could also be worked out by converting the percentage to a decimal. Required Find 16% of 40 (decimal form). Solution 1 16% is the same as 16/100. To find 16% of 40, multiply 16/100 by 40: 16 100 × 40 = 6.4 If you divide 16 by 100 you get 0.16, so 1% of 40 is 0.16, therefore 40 percent must be 6.4. Tutorial note. To divide by 100, you can bring the decimal place in by two places. 2 16% is the same as 0.16. To find 16% of 40, multiply 0.16 by 40: 0.16 × 40 = 6.4 Percentages of amounts can also be found using known facts about percentages. The most helpful of these facts is how to find 10% of an amount. 10% can be written as 10/100 because 10% means 10 out of every 100. Simplifying the fraction 10/100 gives 1/10 (taking out a common factor of 10). This means that 10% is equivalent to dividing by 10 or finding 1/10 of the amount. As finding 10% of a number means to divide by 10, it is common to think that to find 20% of a number you should divide by 20 etc. Remember, to find 10% of a number means dividing by 10 because 10 goes into 100 ten times. Therefore, to find 20% of a number, is to divide by 5 because 20 goes into 100 five times. Once 10% of an amount is known, this can be manipulated to find other amounts such as 5% or 1%, or any amount that is helpful to answer the question (BBC, 2020). 2.4 Calculating percentage increases and decreases One of the starting points for analysis of company performance is calculating the percentage increase or decrease of figures compared to previous years or compared to other companies. Percentage changes are also calculated across all industries as a means of initial overview of the level of change in something and also used by governments, for example, to calculate inflation. To calculate the percentage change, there are two main methods: Formula to learn Difference ( Original ) × 100 4 Paper title

Formula to learn New (Original),−1, × 100 Illustration 2: Percentage increase and decrease Alpha Ltd. is analysing its financial results for the past two years and wants to calculate the percentage change in the following two lines. Required Calculate the percentage increase or decrease in each line. Sales 30 June 2020 30 June 2019 Operating expenses £’s £’s 2,314,000 1,950,200 675,400 723,300 Solution ( Difference ) × 100 Using: Original Sales (2,314,000−1,950,200) × 100 = 18.5% increase 1,950,200 Operating expenses (675,400−723,300) × 100 = 6.62% decrease 723,300 (The answer on the calculator is – 6.62%, the minus indicates a decrease but also just looking at the figures we can see it is a decrease on the prior year) New Using: (Original),−1, × 100 Sales 2,314,000 (1,950,200)−1 × 100 = 18.65% increase Operating expenses 675,400 (723,300)−1( × 100) = 6.62% decrease (Again the answer on the calculator is -6.62% with the minus indicating a decrease) Note in both formulas the word “original” essentially means anything you are comparing to, for example, as well as comparing the results of a company this year compared to previous year/s, you may also be comparing a company to other companies or an industry standard. 1: Basic Mathematics 5

For example: Alpha plc sales this month: £254,000 Beta plc sales this month: £183,000 How much higher are Alpha’s sales compared to Beta, expressed as a percentage? We can use either of the percentage change formulas, but using the second formula: New (Original),−1, × 100 “New” in this context, as previously, is where we are standing from, in this case we are at Alpha in a sense and comparing to Beta. “Original” in this context is what we are comparing to, in this case Beta. So the calculation would be: 254,000 (183,000)−1( × 100) = 38.80% higher I.e. Alpha’s sales are 38.8% higher than those of Beta. If we changed the wording of the question slightly: How much higher are Beta’s sales compared to Alpha, expressed as a percentage? In this case, we are standing at the position of Beta and looking across/comparing to Alpha therefore, the “New” number would be that of Beta and “Original” would be what we are comparing to, i.e. Alpha. So the calculation would be: £183,000 (£254,000)−1, × 100 = 27.95% lower I.e. Beta’s sales are 27.95% lower than Alpha. Note the two percentage figures we have got, 38.8% and 27.95%, are different because although the difference between the two numbers is the same, we are dividing by a different “original” number each time. So, you need to read the question carefully to ensure you put the “new” and “original” numbers in the right place. 2.5 Finding the missing value in a percentages question If we are given incomplete information, as long as we have only one unknown figure it is possible to work back to an original amount. For example: Cheyenne Plc achieved sales of £2,540,000 in the current year. This was a 24% increase on the previous year. What was the sales figure for the previous year? In these questions, start with equating the original figure as being equivalent to 100%. As this year’s sales were 24% higher, the £2,540,000 represents 124% of last year’s sales, which we’ll call “x” as it’s the value we’re trying to find. Putting this into an equation: £2,540,000 = 1.24x (\"1\" = 100%, just as 50% = 0.50) £2,540,000 1.24x = x x = £2,048,387 So last year’s sales must have been £2,048,387. 6 Paper title

We can check this by increasing this figure by 24%: £2,048,387 × 1.24 = £2,540,000 We can also use the same method in the context of a percentage decrease: Sioux Plc achieved sales of £1,560,300 in the current year. This was a 16% increase on the previous year. What was the sales figure for the previous year? Again, we assume that the previous year’s figure is equivalent to 100%. As this years’ sales figure was 16% of the previous year, it must be worth 84% of the previous year’s figure (100% - 16%). Therefore the equation is: £1,560,300 = 0.84x £1,560,300 0.84 = x x = £1,857,500 So last year’s sales must have been £1,857,500. We can check this by decreasing last year’s figure by 16%: £1,857,500 × (1 – 0.16) = £1,560,300 OR £1,857,500 × 84% = £1,560,300 3 Inflation A key economic indicator for a country is its inflation rate, some inflation is a sign of health for an economy but too much inflation can have very adverse consequences. 3.1 What is inflation? Inflation is the rate at which the prices for goods and services increase. It’s one of the key measures of financial wellbeing because it affects what consumers can buy for their money. If there is inflation, money doesn’t go as far. It’s expressed as a percentage increase or decrease in prices over time. For example, if the inflation rate for the cost of a litre of petrol is 2% a year, motorists need to spend 2% more at the pump than 12 months earlier. And if wages don’t keep up with inflation, purchasing power and the standard of living falls. See the image below showing changes in price over the last 30 years for a few standard household items: 1: Basic Mathematics 7

(BBC, 2020) You will see some items such as oranges and bread have more than doubled in price. Fast forward another 30 years and it is likely they could double or even more than double again. Hence, it is important for wages to keep in line with inflation to reflect the erosion of the purchasing power of money. 3.2 What causes inflation? Inflation can be caused by various factors – one of these is demand-pull inflation which is where there is a high amount of demand for particular products/services which in turn encourages suppliers to increase their prices in order to profit from this. Another reason is cost-push inflation which is where suppliers are forced to pay more for a product. If they decide to pass this price increase onto customers then again this causes price increases i.e. inflation. Examples include a bad harvest of a certain crop which pushes up prices or a shortage of electronic components used in electronic devices which pushes up costs as suppliers compete to obtain them. Inflation can also be caused by ‘quantitative easing‘ if too much money is printed. See the following statement from the Bank of England about quantitative easing: “Quantitative easing is a tool that central banks, like us, can use to inject money directly into the economy. Money is either physical, like banknotes, or digital, like the money in your bank account. Quantitative easing involves us creating digital money. We then use it to buy things like government debt in the form of bonds. You may also hear it called ‘QE’ or ‘asset purchase’ - these are the same thing. The aim of QE is simple: by creating this ‘new’ money, we aim to boost spending and investment in the economy.” (Bank of England, 2020) 3.3 How is inflation measured? There are two main measures of inflation, the consumer price index (CPI) and the retail price index (RPI). The Consumer Price Index (CPI) is a measure that examines the weighted average a basket of consumer goods and services, such as transportation, food and medical care. It is calculated by taking price changes for each item in the predetermined basket of goods and averaging them. 8 Paper title

Changes in the CPI are used to assess price changes associated with the cost of living. The CPI is one of the most frequently used statistics for identifying periods of inflation or deflation (Investopedia 2020). Inflation is measured by the Office of National Statistics (ONS). Currently due to depressed demand, the inflation rate is very low, 0.7% (ONS, 2020). The Retail Price Index is similar to the consumer price index except that it also includes housing costs such as mortgage costs and council tax, therefore the RPI is usually higher than the CPI. 3.4 What are inflation rates used for? Inflation rates are used for various reasons. The government may use the CPI for some areas and the RPI for others – see the table below: (Government Actuary’s Department, 2017) 3.5 Calculations with inflation We can use the knowledge from the percentages section earlier to perform calculations related to inflation. 3.5.1 Calculating future costs For example in 2019, inflation in the EU was around 1.44% compared to the previous year (Statista, 2020). Assuming an average basket of goods in the EU cost €55, in 2020 it would cost: €55 x 1.0144 = €55.79 Assuming the inflation had been higher, say at 5%, the cost of a basket of goods after a year would be: €55 x 1.05 = €57.75 3.5.2 Calculating past costs Assuming the price of a basket of goods today is £60 and inflation over the past year has been 8%, we can calculate what the cost of those goods were a year ago: £60 = 1.08x where x = the price of goods a year ago £60 1.08 = £55.55−i.e. the cost of goods a year ago was £55.55 The above could also have been written as: £60 = 108% £60 108 = 0.555 0.555 × 100 = £55.55 We can also calculate the price of goods a month ago: £60 0.08 = £59.60 (1 + ( 12 )) 1: Basic Mathematics 9

3.6 Hyperinflation Hyperinflation commonly occurs when there is a significant rise in money supply that is not supported by economic growth. Simply put, it is caused by dramatically increasing the amount of money in an economy. The increase in money supply is often caused by the government printing and infusing more money into the domestic economy. As there is more money in circulation, prices rise (Corporate Finance Institute, 2020). Hyperinflation has a devastating impact on a country. Currently the inflation rate in Venezuela is around 15,000%! (IMF, 2020) This makes it much too expensive for people to afford goods and services. For example, if a loaf of bread costs £1.09 and inflation was 15,000%, by the end of the year it would now cost: £1.09 + (1.09 x 15,000) = £16,351.09! After another year that same loaf of bread would cost: £16,351.09 + (£16,351.09 x 15,000) = £245,282,701! Hyperinflation causes people to hoard goods including perishable goods and financial institutions collapse. Millions of Venezuelans have migrated to other countries. Governments have tools at their disposal to manage inflation including monetary and fiscal policy. 4 Interest Interest rates are expressed as a percentage so it is essential you are familiar with percentages in order to perform calculations relating to interest rates. 4.1 What is an interest rate? Interest rates are charged by banks on loans and paid by banks on deposits. You will also see interest rates advertised when buying expensive items on credit (buy now, pay later) for example furniture, cars and of course, a house, which is usually the longest credit period ‘item’ someone will purchase. 4.2 Interest and opportunity cost The term ‘opportunity cost‘ refers to the benefit of the next best alternative foregone and occurs whenever there is a limiting factor – i.e. something limiting what you can do. Limiting factors can include money, time and other resources. For example, say you have an option to either go to the cinema or eat out with friends and both options will cost £20 each. If you only have £20 spare, you can’t do both so will have to choose one of these options. If you choose the cinema, you can’t eat out with friends. If you eat out with friends, you can’t go to the cinema. The opportunity cost of choosing the meal would be the lost trip to the cinema, i.e. the next best alternative foregone or given up and vice versa if you chose the cinema. When a bank lends you money, they charge you interest because they could have done something else with that money for example invest it into another bank account or into a project. So they are charging interest to make up for that lost opportunity, i.e. to make up for the opportunity cost. Of course, they usually charge more interest than the opportunity cost in order to make a profit. 4.3 Compound interest Compound interest refers to the principle that when you save money, as well as earning interest on the savings, you also earn interest on the interest itself. Therefore, every year that the money is in your account, you are earning interest on each previous year’s interest. This means that not only are your savings growing over time, but that the rate at which they grow accelerates as well. 10 Paper title

We could see this in action by taking some basic figures – for example, if you deposited £1,000 at a rate of 10%, at the end of year one you would have £1,100, equalling £100 of interest earned. The following year you would earn £110 in interest – 10% of the original capital and 10% of the year one interest. The next year would be £121 and so on (Equifax, 2020). However, compound interest can also apply to loans meaning the amount you pay back is sometimes much more than originally borrowed. 4.4 Compound interest and future values To calculate the present value of a cashflow we can use the formula: Formula to learn PV = FV/(1+r)n Present value = future value divided by 1 + the interest rate, to the power of the number of periods. We will revisit this formula later on, however for now we will rearrange it to help calculate the future value of a cashflow: Formula to learn FV = PV * (1+r)n I.e. future value = present value multiplied by 1 plus the interest rate to the power n, which is the number of time periods e.g. three years or four years. Example Say we invest £12,000 today for four years and the bank offers an interest rate of 6% per year. After four years our investment would be worth: FV = PV * (1+r)n FV = £12,000 * (1+0.06)4 = £15,150 So, we have made £3,150 of interest (£15,150 - £12,000). If we take 6% of £12,000, we get £720 interest per year, multiplying by four years = £2,880. We have made £3,150 interest which is £270 higher (£3,150 - £2,880). This is because of compounding. The impacts of compounding are greater if the present value is higher, interest rates are higher and investment is for a longer period. Of the three factors, often the one that has the most impact is the length of time invested. 4.5 Using the geometric mean to calculate interest rates The geometric mean is the average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio (Investopedia, 2020). Using the geometric mean to calculate interest rates is useful in a scenario where an individual investor or company wants to calculate their average annual returns on an investment which has had varying rates of returns per year. For example, say an investor invests £16,000 into a bank at a certain interest rate and over the next eight years switches their deposit, including the accumulated/compounded interest, to various different banks to ensure they get the highest interest rate. At the end of the eight-year period, their investment will have grown however, calculating the average annual interest rate may seem challenging at first as different amounts have been invested in different banks for varying time periods and at different interest rates. This is where the geometric mean can help. 1: Basic Mathematics 11

Using the same example, if at the end of the eight-year period the amount has grown to £28,536, we can calculate the average annual interest rate using the following formula: Formula 1 New n ( Old ) Where n is the number of time periods. The new number here is £28,536, i.e. what the amount has grown to, and the old is £16,000 i.e. the original amount. n in this case is 8 which is the number of years the amount has been invested. (£28,536/£16,000)1/8 = 1.075, the 1 here represents the original £16,000 investment and the 0.75 represents the annual growth, i.e. the average annual interest rate has been 7.5%. This could be compared to other investments to see if the strategy has been worthwhile. Activity 1: Basic Mathematics Below is an extract from the annual report of Sainsburys plc. (J Sainsbury’s plc, 2020) Required For each of the 12 lines in this consolidated income statement, calculate the percentage change between 2020 and 2019. Use the two “Total” columns in the analysis only i.e. column three and column six For example for Revenue: New ( Old )−1, × 100 28,993 = (29,007)−1, × 100 = −0.5% decrease 12 Paper title

Solution Real life example Percentages are used in many news articles and by politicians to emphasise a point they are making. Look at the following two statements from the same news article: Statement 1 “In a trading update, Tesco said group sales had risen 8% to £13.4bn in the period…” Statement 2 “Tesco reported strong first quarter sales last week. The supermarket said that while the number of trips made by shoppers fell by nearly a third in the 13 weeks to 30 May, the amount being bought rose 64%.” (BBC, 2020) In statement 1, we are told group sales have risen 8% to £13.4bn, but we haven’t been told what they were previously. However, as there is only piece of information missing, previous periods sales, we can work it out using the same method as covered earlier when we looked at finding missing values using percentages. If sales have risen by 8%, that must mean the current sales figure represents 108%. £13.4bn = 1.08x Where x is the missing number - previous periods sales. x = £13.4bn/1.08 = £12.41bn I.e. sales in the previous period was £12.41bn Check: £12.41bn x 1.08 = £13.4bn So if there is only one piece of information missing in a scenario, you can find it using this method. Looking at statement 2 however, we are told the number of shoppers fell by a third, but there are two pieces of information not given – what number they have fallen to and what they were previously. Therefore, we can’t work out either of these figures as there are two unknowns. We are also told the amount being bought rose 64% but again we aren’t told what the new or old figures are, again two unknowns so we can’t calculate either figure. 1: Basic Mathematics 13

One option would be to search online for at least one of the missing figures and use the method described earlier to find the other missing figure, however care has to be taken if using a different source as it may not be accurate. In this case the statements were about Tesco so it would be best to search Tesco’s website directly as the information would be coming directly from the entity it relates to. Statement 3 This is a statement from an article about how Tesla aims to revolutionise battery technology: “The next barrier that is likely to be broken is price. The landmark challenge in the electric vehicle industry is to get a battery costing under $100 (£78) per kilowatt hour. At that point you start to get electric vehicles that are cheaper than the equivalent internal combustion vehicles,” says Seth Weintraub, a US battery technology journalist” (BBC, 2020) Again, here we are told that the aim to is get a battery costing under $100 which is equal to £78, but we are not told what the current cost is or what the aim for the new cost is. Two unknowns so we can’t calculate those figures. However, you may sometimes be able to deduce other information - for example here the article is effectively stating that $100 is equal to £78. We can work out the percentage increase in units of currency you would have to pay if you paid in dollars instead of pounds: New ( Old )−1, × 100 100 = ( 78 )−1, × 100 = 28% I.e. you would pay 28% more units of dollars if you bought the battery using dollars instead of pounds. In fact, if you just leave the calculation as 100/78, this equals 1.28 – this is effectively the exchange rate at the point the article was written i.e. £1 = $1.28. So in an exchange rate, the amount above 1, in this case 0.28, represents by what percentage the base currency is stronger or weaker than the one being compared to. In this case, the dollar is 28% weaker than the pound. 14 Paper title

Skill Checkpoint Check if you can: • Calculate percentage increases and decreases • Find a missing value from a set of information using percentages • Explain the meaning of inflation and hyperinflation • Perform calculations with inflation to calculate future and past values • Calculate future value of an investment using compound interest • Use the geometric mean to calculate interest rates 1: Basic Mathematics 17

References Bank of England (2020). What is quantitative easing? [online] Available at: https://www.bankofengland.co.uk/monetary-policy/quantitative-easing [Accessed 6 July 2020] BBC (2020). How Elon Musk aims to revolutionise battery technology [online] Available at: https://www.bbc.co.uk/news/business-53067009 [Accessed 5 July 2020] BBC (2020). Percentages [online] Available at: https://www.bbc.co.uk/bitesize/guides/z9rjxfr/revision/1 [Accessed 5 July 2020] BBC (2020). Tesco demands supplier price cuts in discount battle [online] Available at: https://www.bbc.co.uk/news/business-53284788 [Accessed 5 July 2020] BBC (2020). What is the UK’s inflation rate? [online] Available at: https://www.bbc.co.uk/news/business-12196322 [Accessed 6 July 2020] Corporate Finance Institute (2020). Hyperinflation [online] Available at: https://corporatefinanceinstitute.com/resources/knowledge/economics/hyperinflation/ [Accessed 6 July 2020] Equifax (2020) Explaining compound interest [online] Available at: https://www.equifax.co.uk/resources/loans_and_credit/explaining-compound-interest.html [Accessed 6 July 2020] Government Actuary’s Department (2017). Measuring price inflation [online] Available at: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/fi le/596837/Inflation_Indices.pdf [Accessed 6 July 2020] International Monetary Fund -IMF (2020). Inflation rate, average consumer prices [online] Available at: https://www.imf.org/external/datamapper/PCPIPCH@WEO/OEMDC/ADVEC/WEOWORLD [Accessed 6 July 2020] Investopedia (2020). Consumer Price Index (CPI) [online] Available at: https://www.investopedia.com/terms/c/consumerpriceindex.asp [Accessed 5 July 2020] Investopedia (2019). Geometric Mean Definition) [online] Available at: https://www.investopedia.com/terms/g/geometricmean.asp [Accessed 6 July 2020] J Sainsburys plc (2020). Annual report and financial statements 2020 [online] Available at: https://www.about.sainsburys.co.uk/~/media/Files/S/Sainsburys/documents/reports-and- presentations/annual-reports/2020/Annual_Report_and_Financial_Statements_2020.pdf [Accessed 6 July 2020] Khan Academy, 2020. Finding percents [online] Available through: https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-percent- problems/e/finding_percents [Accessed 6 July 2020] Khan Academy, 2020. Percent word problems [online] Available through: https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-percent- word-problems/e/percentage_word_problems_1 [Accessed 6 July 2020] Maths Made Easy, 2020. Percentages questions, worksheets and revision [online] Available through: https://mathsmadeeasy.co.uk/gcse-maths-revision/percentages-gcse-revision-and- worksheets/ [Accessed 6 July 2020] Office of National Statistics (2020). Inflation and price indices [online] Available at: https://www.ons.gov.uk/economy/inflationandpriceindices [Accessed 6 July 2020] Statista (2020), Inflation rate in the European Union and the Euro area from 2009 to 2021 [online] Available at: https://www.statista.com/statistics/267908/inflation-rate-in-eu-and-euro-area/ [Accessed 6 July 2020] Study Maths, 2020, Worksheet – Compound interest [online] Available through: https://studymaths.co.uk/workout.php?workoutID=54 [Accessed 6 July 2020] 18 Paper title

Further study guidance It is recommended that learners practise questions related to percentages to strengthen their skills. Opportunities will be given in this module and you can also use the following resources: Maths Made Easy, 2020. Percentages questions, worksheets and revision [online] Available through: https://mathsmadeeasy.co.uk/gcse-maths-revision/percentages-gcse-revision-and- worksheets/ Khan Academy, 2020. Finding percents [online] Available through: https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-percent- problems/e/finding_percents Khan Academy, 2020. Percent word problems [online] Available through: https://www.khanacamy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-percent- word-problems/e/percentage_word_problems_1 Study Maths, 2020, Worksheet – Compound interest [online] Available through: https://studymaths.co.uk/workout.php?workoutID=54 1: Basic Mathematics 19

Key terms Percentage: A percentage is a proportion that shows a number as parts per hundred. The symbol ‘%’ means ‘per cent’. A percentage is a proportion that shows a number as parts per hundred. The symbol ‘%’ means ‘per cent’. 20 Paper title

Activity answers Activity 1: Basic Mathematics (J Sainsburys plc, 2020) Account heading Calculation Percentage change 1 Revenue 2 Cost of Sales (28,993/29,007),-1, x100 0.05% decrease 3 Gross profit 4 Administrative expenses (26,977/26,719), -1, x100 0.98% increase 5 Other income 6 Operating profit (2,016/2,288), -1, x100 11.89% decrease 7 Finance income 8 Finance costs (1,459/1,725), -1, x100 15.42% decrease 9 Share of post-tax (loss) profit from (93/38), -1, x100 144.74% increase joint ventures and associates 10 Profit before tax (650/601), -1, x100 8.15% increase 11 Income tax (expense)/credit 12 Profit for the financial year (32/24), -1, x100 33.33% increase (398/427), -1, x100 6.79% decrease (29/4), -1, x100 625% increase (255/202), -1, x100 26.24% increase (103/16), -1, x100 543.75% increase (152/186), -1, x100 18.28% decrease Although looking at percentage changes are useful to help understand movements, when they are too high, they may become less meaningful. For example, looking at line nine above, there is a 625% increase. If we look at the absolute figures, there was £4m of profit from joint ventures and associates in 2019 and £29m in 2020, so essentially the figure increased by £25m which although is a lot of money, relatively speaking for Sainsburys, it is not extraordinarily high given its revenue is around £29bn. So looking at the absolute figures helps us get a sense of perspective. 1: Basic Mathematics 21

This also highlights that the main function of analysis including percentage changes is to help make information easier to understand. If the technique we use doesn’t help much with this then we may need to use a different or a complementary technique, i.e. the overriding goal is to understand the data, not to use a specific technique. In addition, qualitative data would also be required to help understand why the movements occurred. 22 Paper title