% multiplier. Percentages. New amount (What you end up with) What you have to do. Original amount (What you start with) Using multipliers

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Anna Hutchinson
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1 New amount (What you end up with) What you have to do Original amount (What you start with) 0 N % multiplier Using multipliers What are they? Multipliers are percentages in terms of decimals For example: 70% = % = % = 1.23 Divide your % by 100 to find the multiplier 63% = 42% = 87% = 1% = 107% = Page 1 of 13

2 Why? Multipliers make increasing/decreasing percentages easy. They save time and make you use a calculator. For example: Multiplier Increase 50 by 21% 100% + 21% = 121% As a decimal = x 1.21 = 60.5 Decrease 80 by 14% Increase & Decrease 1. Increase 60 by 12% 2. Increase 140 by 35% 1. Decrease by 28% 3. Decrease 350 by 18% 2. Increase by 33% 4. Decrease 240 by 8% 3. Decrease 350 by 1% 5. Increase by 10% Page 2 of 13

3 Percentage Change So will be given these N We are trying to find this 0 % multiplier 70 is increased to 98 Change: 170 is increased to 242 Change: 70 is decreased to 51 Change: N 0 % multiplier 1. Calculate the percentage change for each of the following: Old amount New amount In each of the following situations, calculate the percentage change: 2. Monthly train tickets are going to increase from 379 to A newspaper sold copies in April and in May. 4. A shop made one week and the next week. 5. A politician received votes in 2005 and votes in the 2010 election Page 3 of 13

4 Reverse percentages There is a 20% Apple The iphone I want is now 500 What was the original cost of the iphone We want to find O the original price We have the N the new price: 500 We have the % multiplier (sort of) It says there is a 20% sale. Original price would be 100%. So if it is 20% off, that would make the new price 80%. Therefore multiplier = 0.80 N 0 % multiplier Calculation: = 625 In a sale, everything is reduced by 30%. If an armchair costs 175 in the sale, what was its price before the sale? A mouse increases its body weight by 15%. If it now weighs 368g, what was the mouse s original weight? Page 4 of 13

5 Reverse percentages practice N 0 % multiplier 1. Apple is having a 20% off sale. After dropping my Ipod in the sink, I thought I should treat myself to a new one. I bought my Ipod for 40. How much was it originally? 2. Christmas is on its way, so the price of Thornton s chocolates has been increased by 15%!! A box of Thornton s continental now costs how much did it cost originally? 3. The price of all oyster card season tickets increased by 4%. The price of a season ticket from zone 1 to zone 4 increased to what was the price before this increase/ 4. A special bottle of Coke contains 10% more than a normal bottle. The special bottle contains 660 ml. How much does the normal bottle contain? 5. Katie gets a 20% pay rise. Her new wage is 264 per week. What was her wage before the pay rise? 6. Ivan Ukhov, the 2012 Olympics high jump gold medallist jumps 2.4 metres. This is 4% lower than the best height he can jump. What is the best height he can jump? 7. A packet of Hobnobs claims to be 24% bigger!! It now contains 31 biscuits. How many did it have before? 8. Delboy sells his goods at Peckham market for making a 15% profit. How much did he pay for the goods when he bought them? 9. Since being on Strictly Come dancing Vanessa Feltz has lost 20% of her body weight. She now weighs 90kg. How much did she weigh before the show? 10. A new Ford fiesta drops in value by 30% in a year. After a year, it is worth Find the price of the car when it was new Page 5 of 13

6 Compound Interest Example: You have a savings account that pays 5%! You save 100. How much do you have after 1 year? How much do you have after 5 years? Section A: Work out the amount gained each year if money is invested at the interest rate specified. Year Amount Interest rate Calculation % Amount at the end of the year % 3 2% 4 2% Year Amount Interest rate Calculation % Amount at the end of the year 2 3.5% 3 3.5% 4 3.5% Section B: Work out the amount gained after n years if money is invested at the interest rate specified. Years (n) Amount Interest rate (pa) Amount after n years % % % % % % Page 6 of 13

Toby invested 7 500 for 2 years in a savings account. He was paid 4% per annum compound interest. How much money did Toby have in his savings account at the end of the 2 years?

5 so in 2 years the value of my house depreciated by 6.5%. a. Is Ibrar right? You must give a reason for your answer. The value of Ibrar s house increases by x% in the third year.

7 Toby invested for 2 years in a savings account. He was paid 4% per annum compound interest. How much money did Toby have in his savings account at the end of the 2 years? Ibrar bought a house for The value of the house depreciated by 4% in the first year. The value of the house depreciated by 2.5 % in the second year. Ibrar says, = 6.5 so in 2 years the value of my house depreciated by 6.5%. a. Is Ibrar right? You must give a reason for your answer. The value of Ibrar s house increases by x% in the third year. At the end of the third year the value of Ibrar s house is b. Work out the value of x. Give your answer correct to 3 significant figures. On 1 st January 2012, Beth invested some money in a bank account. The account pays 2.5% compound interest per year. On 1 st January 2013 Beth withdrew 1000 from the account. On 1 st January 2014 she had in the account. Work out how much money Beth originally invested in the account Page 7 of 13

8 Ian invested an amount of money at 3% per annum compound interest. At the end of 2 years the value of the investment was a. Work out the amount of money Ian invested.... Noah has an amount of money to invest for five years. Saver Account 4% per annum compound interest Investment account 21% interest paid at the end of 5 years Noah wants to get the most interest possible. Which account is best? You must show how you got your answer. An amount of money was invested for 8 years. It earned compound interest at 2.5% per year. After 8 years the total value of the investment was Tom is trying to work out the total interest earned Interest for 8 years = x x 8 State what is wrong with Tom s method. Work out the total interest earned Page 8 of 13

9 Answers 63% = % = % = % = % = 0.01 Decrease 80 by 14% = 68.8 Increase & Decrease 6. Increase 60 by 12% Increase 140 by 35% Decrease by 28% Decrease 350 by 18% Increase by 33% Decrease 240 by 8% Decrease 350 by 1% Increase by 10% is increased to 98 40% increase 170 is increased to % increase 70 is decreased to 51 27% decrease 1. Calculate the percentage change for each of the following: Old amount New amount % increase % increase % decrease % increase % decrease In each of the following situations, calculate the percentage change: 2. Monthly train tickets are going to increase from 379 to % increase 3. A newspaper sold copies in April and in May. 5.8% decrease 4. A shop made one week and the next week. 9.3% increase 5. A politician received votes in 2005 and votes in the 2010 election. 6.0% decrease Page 9 of 13

10 In a sale, everything is reduced by 30%. If an armchair costs 175 in the sale, what was its price before the sale? 250 A mouse increases its body weight by 15%. If it now weighs 368g, what was the mouse s original weight? 320g Reverse percentages practice 1. Apple is having a 20% off sale. After dropping my Ipod in the sink, I thought I should treat myself to a new one. I bought my Ipod for 40. How much was it originally? Christmas is on its way, so the price of Thornton s chocolates has been increased by 15%!! A box of Thornton s continental now costs how much did it cost originally? The price of all oyster card season tickets increased by 4%. The price of a season ticket from zone 1 to zone 4 increased to what was the price before this increase/ A special bottle of Coke contains 10% more than a normal bottle. The special bottle contains 660 ml. How much does the normal bottle contain? 600ml 5. Katie gets a 20% pay rise. Her new wage is 264 per week. What was her wage before the pay rise? Ivan Ukhov, the 2012 Olympics high jump gold medallist jumps 2.4 metres. This is 4% lower than the best height he can jump. What is the best height he can jump? 2.5m 7. A packet of Hobnobs claims to be 24% bigger!! It now contains 31 biscuits. How many did it have before? Delboy sells his goods at Peckham market for making a 15% profit. How much did he pay for the goods when he bought them? Since being on Strictly Come dancing Vanessa Feltz has lost 20% of her body weight. She now weighs 90kg. How much did she weigh before the show? 112.5kg 10. A new Ford fiesta drops in value by 30% in a year. After a year, it is worth Find the price of the car when it was new Page 10 of 13

11 Compound Interest Example: You have a savings account that pays 5%! You save 100. How much do you have after 1 year? 105 How much do you have after 5 years? Section A: Work out the amount gained each year if money is invested at the interest rate specified. Year Amount Interest rate Calculation Amount at the end of the year % 1530 x % x % x % x Year Amount Interest rate Calculation Amount at the end of the year % 2999 x % x % % Section B: Work out the amount gained after n years if money is invested at the interest rate specified. Years (n) Amount Interest rate (pa) Amount after n years % 720 x 1.04n % 400 x 1.03n % x 1.021n % x 1.064n % x n % x 1.045n Page 11 of 13

12 Toby invested for 2 years in a savings account. He was paid 4% per annum compound interest. How much money did Toby have in his savings account at the end of the 2 years? 7500 x = 8112 Ibrar bought a house for The value of the house depreciated by 4% in the first year. The value of the house depreciated by 2.5 % in the second year. Ibrar says, = 6.5 so in 2 years the value of my house depreciated by 6.5%. a. Is Ibrar right? You must give a reason for your answer. No. Multiplier is 0.96 x = so 6.4% decrease The value of Ibrar s house increases by x% in the third year. At the end of the third year the value of Ibrar s house is b. Work out the value of x x = so worth that after 2 years = so x=6.8 Give your answer correct to 3 significant figures. On 1 st January 2012, Beth invested some money in a bank account. The account pays 2.5% compound interest per year. On 1 st January 2013 Beth withdrew 1000 from the account. On 1 st January 2014 she had in the account. Work out how much money Beth originally invested in the account Ian invested an amount of money at 3% per annum compound interest. At the end of 2 years the value of the investment was b. Work out the amount of money Ian invested Page 12 of 13

13 Noah has an amount of money to invest for five years. Saver Account Investment account 4% per annum compound interest 21% interest paid at the end of 5 years Noah wants to get the most interest possible. Which account is best? 1.045=1.216 which is > 1.21 so saver account is better You must show how you got your answer. An amount of money was invested for 8 years. It earned compound interest at 2.5% per year. After 8 years the total value of the investment was a. Tom is trying to work out the total interest earned Interest for 8 years = x x 8 State what is wrong with Tom s method. Didn t use compound interest Work out the total interest earned = So interest = = Page 13 of 13

Bridging Units: Resource Pocket 8

Bridging Units: Resource Pocket 8 Growth and Decay Students may be familiar with the concepts of growth and decay from science lessons. This is a natural progression from the work in resource pocket 1