Oil prices rise by 4% The numerator is 45 and the denominator is 100

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1 2 CHAPTER 3. 3 A head Scatter graphs CHAPTER 3 Percentages CHAPTER 2. Percentages ALL PRICES REDUCED BY % DAILY BLAH Oil prices rise by 4% thank you for your contribution this year. Your salary will increase by 6% The pictures show examples of the use of percentages. Per cent means out of. 3 per cent means 3 out of or as a fraction 3 3 per cent is written as 3%. Learn these percentages with their fraction and decimal equivalents. Percentage Fraction Decimal % % 2% 2 2 2% % 2 7% % Example Write each of these percentages as i a fraction in its simplest form ii a decimal a 4% b 3% c 7 2 % Solution 4 a i 4% The numerator is 4 and the denominator is is the highest common factor of 4 and Divide both 4 and by to get and 2 do not have a common factor and so 9 2 is in its simplest form. 4 ii 4%.4 b i 3% 3 3 ii 3%.3 Change the fraction into a decimal. 3 cannot be simplified as there is no number that divides exactly into both 3 and Write the 3 in the hundredths column and a zero in the tenths column. 74

2 2. Percentages CHAPTER 2 c i 7 2 % % means 7 2 out of Multiply both 7 2 and by 2 to change the 7 2 to a whole number is the highest common factor of 3 and 2 Divide both 3 and 2 by to get and 4 do not have a common factor and so 7 4 is in its simplest form. ii 7 2 % 7.% 7. Method %.7 Method %.7 Method is the same as. To work out 7. without a calculator move each figure of the 7. two places to the right as described in Section 7.. Alternatively multiply both 7. and by and then write 7 as a decimal. With a calculator work this out by keying in 7. To find a percentage of a quantity the percentage should first be written as a fraction or a decimal. Example 2 a Find 2% of 6 b Find 6% of 7 Solution 2 a If a percentage can be written as a simple fraction then use this fraction to work out a percentage of a quantity. 2% This fact should be known. To find 4 of 6, divide 6 by 4 2% of 6 4 of 6 is and 4 6 is also 7

3 CHAPTER 2 Percentages b Method % of 7 2 Divide both 7 and by 2 Divide both 6 and 4 by 4 Method 2 6% Key in 6% of Example 3 Colin invests 8 The interest rate is.2% per year. How much interest will Colin receive after year? Solution 3.2% of Colin receives 96.2 interest after year. Key in. 2 8 or change.2% to a decimal and work out.2 8 As the answer is an amount of money, there must be two figures after the decimal point. Exercise 2A Write each percentage as a fraction. a 79% b 9% c 7% d % e 7% 2 Write each percentage as a fraction in its simplest form. a % b 2% c 7% d 3% e 2% f 84% g 9% h 2 2 % i 7 4 % j 4.2% 3 Write each percentage as a decimal. a 63% b 98% c 7% d 2% e 6% f 23.% 4 28% of children walk to school. What fraction of children walk to school? Give your fraction in its simplest form. 92% of students in a class have a mobile telephone. Work out the fraction of students that do not have a mobile telephone. Give your fraction in its simplest form. 6 Work out a % of 3 b 2% of 4 c % of 84 d % of 6 e 2% of 2 f 2% of 3 g % of 8 h % of i 2% of j 7% of 4 76

4 2.2 Increases and decreases CHAPTER 2 7 Work out a 2% of 3 b 2% of 6 g c 2% of 8 cm d 7% of 4 m e 8% of 3 f 4% of 7 g g 2% of 3 kg h 6% of 3 km 8 Tony earns 4. He gets a bonus of %. Work out Tony s bonus. 9 There are shop assistants in a large store. 8% of the shop assistants are male. How many of the shop assistants are male? Danya invests 2 The interest rate is 4% per year. How much interest will she receive after year? In Year there are 4 students. 84 of these students are girls. % of the girls and % of the boys attend Spanish lessons. What fraction of these Year students attend Spanish lessons? Give your fraction in its simplest form. 2 Work out a 34% of m b 2% of 36 c % of 32.4 d 8% of 62 kg e 9% of 23 f 4% of 9 m g 4.2% of 6 km h 3.2% of 4 i 7 2 % of 3 j 6 4 % of 4 cm 3 Anna scored 6% in a test. The test was out of 4 marks. How many marks did Anna score? 4 There are 24 students in a school. 7% of the students in the school wear glasses. How many of the students wear glasses? A shop has 46 DVDs. 23% of the DVDs are thrillers. How many of the DVDs in the shop are thrillers? 6 The price of a washing machine is 2 Ahmid pays a deposit of 3% of the price. Work out his deposit. 7 Martin invests 3 The interest rate is 4.3% per year. How much interest will he receive at the end of year? 2.2 Increases and decreases A multiplier is a single number that an amount is multiplied by in order to increase or decrease that amount. Example 4 Write down the multiplier that can be used to a increase an amount by 9% b decrease an amount by 2% Solution 4 a % 9% 9% 9% 9.9 The multiplier that can be used to increase an amount by 9% is.9 b % 2% 88% 88 88%.88 Think of the original amount as %, add 9% to the original amount. Write the new percentage as a fraction. Divide by to write the fraction as a decimal. The original amount is %, subtract 2% from the original amount. Write the new percentage as a fraction. Divide by to write the fraction as a decimal. The multiplier that can be used to decrease an amount by 2% is.88 77

5 CHAPTER 2 Percentages These examples show how to increase and decrease amounts by a given percentage, including the use of multipliers. Example Hugh s salary is 2 a year. His salary is increased by 4% Work out his new salary. Solution Method 4% of This is the increase in Hugh s salary. His increase in salary is 2 26 Hugh s new salary is 26 Method 2 % 4% 4% 4% Hugh s new salary is 26 Add the increase to his original salary. His new salary is 4% of 2.4 is the multiplier. Find 4% of 2 (This increases 2 by 4%) Example 6 The value of a car depreciates by % each year. The value of a car when new is 4 Work out the value of the car after year. Solution 6 Method % of Depreciates means that the value of the car decreases. This is the decrease in the value of the car. Write the percentage as a fraction. Work out the multiplication Value after year 9 The depreciation in year is 2 Subtract to work out the new value. 78

6 2.2 Increases and decreases CHAPTER 2 Method 2 % % 8%.8 4 8%.8 9 The final value is 8% of the original value..8 is called the multiplier. Find 8% of 4 to reduce 4 by % With this method the actual decrease in the value is not found. Value after year 9 Exercise 2B Write down the multiplier that can be used to work out an increase of a 64% b 3% c 4% d 4% e 3.4% f 2 2 % g % h 4% 2 Write down the multiplier that can be used to work out a decrease of a 7% b 2% c 6% d 27% e.6% f 2 2 % g 7 4 % h.8% 3 Write down the percentage increase represented by each of the following multipliers. a.6 b.43 c.24 d. e.3 f.89 g 3 h 2. 4 Write down the percentage decrease represented by each of the following multipliers. a.8 b.94 c.4 d.7 e.6 f.92 g.77 h.99 Jeevan earns 2 per week. He gets a wage rise of %. How much does Jeevan earn per week after his rise? 6 In a sale all prices are reduced by %. Work out the sale price of each of the following % OFF CD Player normally 4 Computer normally 2 Television normally 3 CD a a television set that normally costs 3 b a CD player that normally costs 4 c a computer that normally costs 2 7 The table shows the salaries of three workers. Each worker receives a % salary increase. Work out the new salary of each worker. Helen 2 Tom 24 Sandeep 32 79

7 CHAPTER 2 Percentages 8 8 Hanni invests 3 The interest rate is 4% per year. How much will Hanni have in his bank account at the end of year? 9 The price of a computer is 4 Its price is reduced by % in a sale. Work out the sale price of the computer. Jenny puts 6 into a bank account. At the end of year 3.% interest is added. How much is in her account at the end of year? A holiday normally costs 8 It is reduced by 2%. How much will the holiday now cost? 2 A year ago, the value of Richard s house was 8 Its value has now increased by 9%. Work out the value of Richard s house now. 3 Ria buys a car for 23 The value of the car depreciates by 2% each year. Work out the value of the car at the end of year. 4 Value Added Tax (VAT) is charged at a rate of 7 2 %. A builder s bill is 962 before VAT is added. What will the bill be after VAT has been added? Pat normally pays 4 for her train fare. All train fares are increased by 9%. How much will Pat now have to pay? 6 The total price of a radio is 46.8 plus VAT at 7.%. Work out the total price of the radio. To write one quantity as a percentage of another quantity: write down the first quantity as a fraction of the second quantity change the fraction to a percentage Example 7 a Change out of 2 to a percentage. Do not use a calculator. b Change 23 out of 4 to a percentage. You may use a calculator. Solution 7 a 2 2 % out of 2 % Write the first number as a fraction of the second number. Change 2 to a fraction with a denominator of b Write the first number as a fraction of the second number % Change the fraction to a decimal and then to a percentage out of 4 7.% In a 2 and in b So to change a fraction to a percentage, multiply the fraction by

8 2.2 Increases and decreases CHAPTER 2 Example 8 Express 4 cm as a percentage of 2 m. Solution 8 There are two different types of units in the question centimetres and metres. Quantities must have the same units before the percentage is found. In this case express both lengths in centimetres. 2m2 cm Use m cm % 2 4 cm is 22.% of 2 m. Percentage problems sometimes involve percentage profit or percentage loss where profit Percentage profit % origin al amount loss Percentage loss % origina l amount Example 9 Karen bought a car for 2 One year later she sold it for 84 Work out her percentage loss. (Do not use a calculator.) Solution % 2 Her percentage loss is 3% Example Write 4 as fraction of 2 4 Multiply 2 by to change it to a percentage. Subtract the selling price from the original price to find her loss. loss Write down the fraction origin al price It is not necessary to simplify the fraction yet. 36 Multiply 2 by to change it to a percentage. Tony bought a box of 24 oranges for 4 He sold all the oranges for 2p each. Work out his percentage profit. Solution In this question there are two different units, pounds and pence. Either pounds or pence may be used but it must be the same throughout the question Work out the total amount in pence Tony received from selling all the oranges p profit % 4 Percentage profit 26% Subtract the original price from the selling price to find his profit in pence. profit Write down the fraction working in pence. orig inal price 4 Multiply 4 by to change it to a percentage. 8

9 CHAPTER 2 Percentages An index number is used to give a measure of how a value has changed. The index number is based on using to represent the value in a particular year. For example in 24 a man s daily pay was 2 In 2 it was as a percentage of 2 is 2 8 4% 2 Taking 24 as the base year with an index number of, the index number in 2 is 4 Example In 2 a holiday cost 6 In 2 an identical holiday cost 728 a Express the cost of the holiday in 2 as a percentage of the cost in 2 b If the index number in the year 2 is write down the index number of the holiday in 2 Solution a % 6 The price in 2 is 2% of the price in the year 2 b The index number is 2 To write down the index number just omit the percentage sign from the answer to a. Example 2 In 2 a Deltan computer cost In 26 the Deltan computer cost 4 Taking 2 as the base year with an index number of find the index number in 26 Solution 2 4 9% The index number in 26 is 9 Express the cost of the computer in 26 as a percentage of its cost in 2 Exercise 2C Write a 3 as a percentage of 6 b 2 kg as a percentage of 8 kg c 4p as a percentage of p d 8 cm as a percentage of 4 cm e 8 as a percentage of 4 f 3 as a percentage of 3 g 7 kg as a percentage of 3 kg h 3m as a percentage of 2 m i 9 km as a percentage of km j 36 as a percentage of 48 2 Write a 2p as a percentage of 2 b 2 cm as a percentage of m c 6 g as a percentage of kg d 8 m as a percentage of km e 6p as a percentage of 2.4 f mm as a percentage of 6 cm g 36 minutes as a percentage of hour h cm as a percentage of 4 m 3 Janet scored 36 out of 4 in a German test. Work out her score as a percentage. 4 In Year there are 24 students. of these students are boys. What percentage of Year students are a boys b girls? 82

10 2.2 Increases and decreases CHAPTER 2 Jerry took 6 bottles to a bottle bank. 27 of the bottles were green. What percentage of the bottles were green? 6 There are 8 pages in a book. 3 of the pages have pictures on them. What percentage of the pages in the book have pictures on them? 7 Mr Potter buys a house for 2 Five years later the value of the house has increased to 26 Work out the percentage increase in the value of the house. 8 A shopworker s wage was 24 per week. After a pay rise her wage is 24.4 Work out the percentage increase. 9 Trevor bought a new car for 6 He sold it after two years for 2 Work out his percentage loss. In a sale the price of a clock is reduced from 32 to 27.2 Work out the percentage reduction. In a survey 44 out of 2 people surveyed said that they were going on holiday in the summer. a What percentage were going on holiday? b What percentage were not going on holiday? 2 Rob bought a crate of 4 melons for 3 He sold all the melons for. each. Work out his percentage profit. 3 A box of cereal weighs 7 g. It contains 2 g of dried fruit. What percentage of the cereal is dried fruit? 4 A 4 g serving of cereal contains 8 g of protein, 24 g of carbohydrates, 4. g of fat and 3. g of fibre. What percentage of the serving is a protein b carbohydrates c fat d fibre? In 2 the value of a house was 8 In 2 its value was 2 a Work out the value of the house in 2 as a percentage of the value of the house in 2 b If the index number in 2 is write down the index number in 2 6 In 2 a train journey cost 8 In 23 the same train journey cost 98.6 In 2 the same train journey cost 7.9 a Work out the cost of the train journey in 23 as a percentage of the cost of the train journey in 2 b Write down the index number in 23 based on an index of in 2 c Work out the cost of the train journey in 2 as a percentage of the cost of the train journey in 2 d Write down the index number in 2 based on an index of in 2 7 In 22 the price of an Olympic camera was 2 In 23, the price of the camera was 22 and in 24 the price of the camera was 22 a Work out the price of the camera in 23 as a percentage of its price in 22 b Based on an index of in 22 i write down the index number in 23 ii find the index number in 24 83

11 CHAPTER 2 Percentages 2.3 Use of multipliers Banks and building societies pay compound interest. At the end of the first year, interest is paid on the money in an account. This interest is then added to the account. At the end of the second year interest is paid on the total amount in the account, that is, the original amount of money plus the interest earned in the first year. At the end of each year, interest is paid on the total amount in the account at the start of that year. If 2 is invested in a bank account for one year and interest is paid at a rate of % then, using the multiplier. after year there will be a total of (2.) in the account after 2 years there will be a total of ((2.).) in the account after 3 years there will be a total of (((2.).).) in the account. To find the amount in the account after 3 years the original 2 is multiplied by... which is equivalent to is the single number that 2 is multiplied by to find the amount in the bank account after 3 years. In general to work out the amount in a savings account after n years if interest is paid at r % per annum, multiply the original amount by r n Example 3 4 is invested for 2 years at % per annum compound interest. Work out the total interest earned over the 2 years. Solution 3 Method using multipliers % % % %. Work out the multiplier for an increase of % Multiply the original amount by. 2 to find the amount in the account after 2 years. Subtract the original amount to find the interest. The total interest earned over the 2 years is 4 Method 2 repeated increase Work out the interest in the first year. Add the interest to the original amount. Work out the interest in the second year. Find the total interest. The total interest earned over the 2 years is 4 84

12 2.3 Use of multipliers CHAPTER 2 Example 4 a Each year the value of a car depreciates by 3%. Find the single number as a decimal that the value of the car can be multiplied by to find its value at the end of 4 years. b The value of a house increases by 6% of its value at the beginning of the year.the next year its value decreases by 3% of its value at the start of the second year. Find the single number as a decimal that the original value of the house can be multiplied by to find its value at the end of the 2 years. Solution 4 a % 3% 7% Find the multiplier that represents a decrease of 3%. 7 7% is the single number b % 6% 6% 6% 6.6 % 3% 97% 97 97% is the single number Example The value of a machine when new is 8 The value of the machine depreciates by % each year. Work out its value after 3 years. Solution Method using multipliers % % 9% Work out the multiplier for a decrease of 9%. 9% Multiply the value when new by.9 3 to find the value after 3 years. The value of the machine after 3 years is 832 Method 2 repeated decrease The value of the machine after 3 years is 832 The depreciation is over 4 years so the single multiplier is.7 raised to the power of 4 Find the multiplier for an increase of 6%. Find the multiplier for a decrease of 3%. The value increases and then decreases so find the product of the two multipliers. Work out the depreciation in the first year. Work out the value of the machine at the end of the first year. Work out the depreciation in the second year. Work out the value of the machine at the end of the second year. Work out the depreciation in the third year. Work out the value of the machine at the end of the third year. 8

13 CHAPTER 2 Percentages Example 6 The population of an island is 6 The population is increasing at a rate of 8% per year. After how many years will the population first exceed? Solution 6 % 8% 8% Find the multiplier that represents an increase of 8%. Choose a number of years to use in a first trial, say Work out the population after years. The population is less than Work out the population after 7 years. The population is still less than Work out the population after 8 years The population is now greater than The population first exceeds after 8 years. Exercise 2D Work out the multiplier as a single decimal number that represents a an increase of 2% for 3 years b a decrease of % for 4 years c an increase of 6% for 2 years d a decrease of % for 3 years e an increase of 2% followed by a decrease of 8% f a decrease of 8% followed by a decrease of 2% g an increase of 4% followed by an increase of 2% h a decrease of 3% followed by a decrease of 2% 2 Ben says that an increase of 4% followed by an increase of 2% is the same as an increase of 6%. Is Ben correct? You must give a reason for your answer. 3 is invested for 2 years at % per annum compound interest. Work out the total amount in the account after 2 years. 4 3 is invested for 4 years at 7% per annum compound interest. Work out the total interest earned over the 4 years. A motorbike is worth 6 Each year the value of the motorbike depreciates by 3%. Work out the value of the motorbike at the end of three years. 6 A house is worth 7 Its value increases by 6% each year. Work out the value of the house after a 3 years b years c 2 years. Give your answers to the nearest pound. 7 The population of a town is 6 The population is increasing at a rate of 3% per year. Work out the population of the town after 4 years. 86

14 2.4 Reverse percentages CHAPTER 2 8 Mrs Bell buys a house for 6 In the first year the value of the house increases by 6%. In the second year the value of the house decreases by 4% of its value at the beginning of that year. a Write down the single number as a decimal that the original value of the house can be multiplied by to find its value after 2 years. b Work out the value of the house after the 2 years. 9 Jeremy deposits 3 in a bank account. Compound interest is paid at a rate of 4% per annum. Jeremy wants to leave the money in the account until there is at least 4 in the account. Calculate the least number of years Jeremy must leave his money in the bank account. is invested in a savings account. Compound interest is paid at a rate of.% per annum. Calculate the least number of years it will take for the original investment to double in value. 2.4 Reverse percentages Multipliers can be used to find the original quantity if the final value after a percentage increase or decrease is known. Example 7 In a sale all the jackets are reduced by 2%. The sale price of a jacket is 33.6 Work out the original price of the jacket. Solution 7 Method using multipliers % 2% 8% 8.8 Let the original price be x x x The original price of the jacket was 42 Find the multiplier for a decrease of 2%. The original price was multiplied by.8 to give 33.6 Write this as an equation. Solve the equation. (Check: ) Method 2 using percentages % 2% 8% represents 8% of the original price Divide 33.6 by 8 to find the value of % The original price is % so multiply the amount that represents % by The original price of the jacket was 42 (Check: ) 87

15 CHAPTER 2 Percentages Example 8 The price of a new washing machine is 376 This price includes Value Added Tax (VAT) at 7 2 %. Work out the cost of the washing machine before VAT was added. Solution 8 Method using multipliers % 7.% 7.% 7..7 Let the original price be x x x.7 32 The original cost was increased by 7.% so find the multiplier for an increase of 7.%. The original cost was multiplied by.7 to give 376 Write this as an equation. Solve the equation. The cost of the washing machine before VAT was added was 32 Method 2 using percentages % 7.% 7.% The cost of the washing machine before VAT was added was 32 (Check: ) 376 represents 7.% of the original cost. Divide 376 by 7. to find the value of %. The original cost is % so multiply the amount that represents % by (Check: ) Exercise 2E In a sale all the prices are reduced by 2%. The sale price of a dress is 3 Work out the normal price of the dress. 2 Employees at a firm receive a pay increase of 4%. After the pay increase Linda earns How much did Linda earn before the pay increase? 3 The price of a new television set is 329 This price includes Value Added Tax (VAT) at 7 2 %. Work out the cost of the television set before VAT was added. 4 A company bought a new lorry. Each year the value of the lorry depreciates by 2%. After year, the lorry was worth 26 Work out the original price of the lorry. A holiday is advertised at a price of 43 This represents a 3% saving on the brochure price. Work out the brochure price of the holiday. 6 Kunal pays tax at a rate of 22%. After he has paid tax Kunal received 4.4 per week. How much does Kunal earn per week before he pays tax? 7 A large firm hires 3% more workers which brings its total number of workers to How many workers did the firm have before the increase? 88

16 Chapter summary CHAPTER 2 8 In year the population of an island increased by 3.2% to Work out the population of the island before the increase. 9 Tasha invests some money in a bank account. Interest is paid at a rate of 8% per annum. After year there is 29.6 in the account. How much money did Tasha invest? Javed invests some money in a bank account. Compound interest is paid at a rate of 4% per annum. After 2 years there is in the account. How much did Javed invest? Chapter summary You should now know that: per cent means out of 3 per cent means 3 out of or as a fraction, 3 3 per cent is written as 3% Percentage Fraction Decimal %. %. 2% % % 2. 7% % an index number is used to give a measure of how a value has changed. The index number is based on using to represent the value in a particular year. a multiplier is a single number that a quantity can be multiplied by in order to increase or decrease the quantity. You should also be able to: work out the percentage of a quantity by changing the percentage into a fraction and multiplying the quantity by this fraction change a fraction into a percentage by multiplying the fraction by % work out the percentage profit or percentage loss profit Percentage profit % origin al amount loss Percentage loss % origina l amount work out the amount in a savings account if interest is paid at r% for n years by multiplying the original amount by r n find the original quantity, given the final value after a percentage increase or decrease by dividing by the original multiplier. 89

17 CHAPTER 2 Percentages Chapter 2 review questions a Write.4 as a percentage. b Write 3 4 as a percentage. c Write 3% as a fraction in its simplest form. (388 January 23) 2 Work out 2% of 6 3 a Write 4 cm as a percentage of m b Write 3 g as a percentage of 2 kg. 4 a Change 7 8 to a decimal. b Use your answer to part a to write 7 8 as a percentage. There are 8 students at Prestfield School. 44 of these students were absent from school on Wednesday. a Work out how many students were not absent on Wednesday. Trudy says that more than 2% of the 8 students were absent on Wednesday. b Is Trudy correct? Explain your answer. 4% of these 8 students are girls. c Work out 4% of 8 There are 76 students in Year d Write 76 out of 8 as a percentage. (387 June 24) 6 Ben bought a car for 2 Each year the value of the car depreciated by %. Work out the value of the car 2 years after he bought it. 7 Work out 34% of (387 June 23) 8 Jo got 36 out of 8 in an English test. a Work out 36 out of 8 as a percentage. Jo got 6% of the total number of marks in a French test. Jo got 39 marks. b Work out the total number of marks for the French test. (38 June 2) 9 Jane buys a box of 2 pens for 8. She sells all the pens at 36p each. Work out her percentage profit. Annie bought 24 cans of drink for 2 pence each. At a fete she sold half of these cans of drink for 4 pence each. At a disco she sold 8 of these cans of drink for 3 pence each. She gave the rest of the cans of drink away. Work out the percentage profit that Annie made on the 24 cans of drink. A can of drink costs 32p. The cost of the can of drink is increased to 38p. Jenny calculates that this is a percentage increase of 9%. Is Jenny s percentage correct? You must show how you reached your decision. (388 January 23) 9

18 Chapter 2 review questions CHAPTER 2 2 In a sale normal prices are reduced by 2%. The normal price of a camera is 79 Work out the sale price of the camera. (38 May 22) 3 The depreciation of a car is 2% each year. The value of the car is 8 Work out the value of the car at the end of 3 years. 4 2 is invested for 3 years at % per annum compound interest. Work out the total interest earned over the 3 years. (38 November 2) is invested for 3 years at 4% per annum compound interest. Work out the total interest earned over the 3 years. (38 June 2) 6 The price of a new television is 423 This price includes Value Added Tax (VAT) at 7 2 %. a Work out the cost of the television before VAT was added. At the end of each year the value of a television has fallen by 2% of its value at the start of the year. The value of a television was 423 at the start of the first year. b Work out the value of the television at the end of the third year. Give your answer to the nearest penny. (38 June 2) 7 In a sale all prices are reduced by %. The normal price of a jacket is 42 SALE Syreeta buys the jacket in the sale. a Work out the sale price of the jacket. % OFF In the same sale, Winston pays.64 for a shirt. all prices b Calculate the normal price of the shirt. (38 June 2) 8 A company bought a van that had a value of 2 Each year the value of the van depreciates by 2%. a Work out the value of the van at the end of 3 years. The company bought a new truck. Each year the value of the truck depreciates by 2%. The value of the truck can be multiplied by a single number to find its value at the end of 4 years. b Find this single number as a decimal. (387 June 24) 9 Bill invests on st January 24 at a compound interest rate of R% per annum. The value, V, of this investment after n years is given by the formula V (.4) n a Write down the value of R. b Use your calculator to find the value of Bill s investment after 2 years. (387 June 2) 9