Year 9 Percentages Dr J Frost jfrosttiffin kingston

Year 9: Percentages Dr J Frost (jfrost@tiffin. kingston. sch. uk) Last modified: 24 th December 2014

Overview 1 27% of 420 (using a calculator and without using a calculator) 2 The cost of car originally worth £ 15, 000 but after losing 15% of its value. 3 The value of saving account BEFORE it increased by 35% to £ 16, 000 4 The value of an ISA with a principal of £ 1000, after accruing 5 years of interest at 3% p. a. 5 What tax do I pay on £ 57, 000?

The Key to Percentages It’s all about identifying a decimal multiplier! What would you multiply by in order to: ? ? ?

Quickfire Exercises 1 Effect Multiplier Increase by 47% x 1. 47 Depreciate by 36% x 0. 64 Find 30% of the value. x 0. 3 Increase by 110% x 2. 1 Decrease by 10%, then increase by 10% x 0. 99 ? Increase by 25%, then decrease by 20%. x 1 ? 2 ? ? N ? ? 3 ?

WITHOUT a calculator 35% of £ 64

Finding the percentage change Formula: 1 2 3 4 5 6 ? ? ?

Exercise A 4 [IMC] A shop advertised “Everything half price in 1 a our sale”, but also now advertises that there is “An additional 15% off sale prices”. Overall, this is equivalent to what reduction on the original prices? 57. 5% ? b ? ? 5 [IMC] Inspector Remorse had a difficult year in 2004. A crime wave in Camford meant that he had 20% more cases to solve than in 2003, but his success rate dropped. In 2003, he solved 80% of his cases, but in 2004 he solved only 60% of them. What was the percentage change in the number of cases he solved in 2004 compared with 2003? Down by 8% c ? 2 a b c 3 a b ? ? ? ? ? [STMC] In a sale, the price of a computer is N reduced by 20%. At this reduced price the shopkeeper still makes a profit of 20%. What would have been his percentage profit if the computer had been sold at full price? 50% ? ?

Compound changes I put £ 1000 into an account with 3% interest p. a. How much is there in the account after 7 years? (Hint: again, it’s all about the appropriate multiplier!) ? My house is worth £ 250, 000. However, due to the economic crisis, the value depreciates by 10% each year. How much is it worth 5 years later ?

Compound vs ‘Simple’ interest This rarely comes up in GCSE exams, but you should appreciate the difference between compound and simple interest. If the principal of a bond is £ 1000, and the interest rate 10% p. a. , find the value after 5 years using: Compound interest: ? Simple interest: ?

Exercise B 5 1 ? 2 ? N 1 ? 3 ? N 2 ? ? 4 N 3 ? ?

Reverse Percentages We’ve so far always multiplied by the multiplier in order to find the new value. But what if we wanted to find the original value before the percentage change? ?

Example After a bloody fight with George, Fareed lost 30% of his body’s blood. He now only had 5. 6 pints of blood left. How much blood did he originally have? Method 1: Using multipliers ? Method 2: Starting at 100% ?

Test Your Understanding [Edexcel GCSE June 2013] The normal price of a television is reduced by 30% in a sale. The sale price of the television is £ 350. Work out the normal price of the television. Method 2: 70% is £ 350 ? 10% is £ 50 100% is £ 500 [Edexcel GCSE Nov 2013] In a sale normal prices are reduced by 20%. A washing machine has a sale price of £ 464. By how much money is the normal price of the washing machine reduced? ?

To reverse or not to reverse? That is the question. Shakespeare bought 375 quills this year. This was 25% less than last year. How many did he previously buy? Don’t Reverse Last year a performance of The Merchant of Venice took in 60 farthings. This year it took in 15% less. How much was made this year? Don’t Reverse Don’t Reverse A cutlass with 20% VAT costs £ 162. What was the cost without VAT? Mecrutio sues Romeo for 150 farthings for mortal injuries inflicted. However, after realising he’s being a bit of a douche, he decides to lower this amount by 36%. How much did he sue Romeo for?

More examples ? ?

Exercise C 6 1 ? 2 ? 7 ? ? 3 8 ? 4 ? ? 9 5 ? ?

REVISION VOTE WITH YOUR DIARIES RED ORANGE GREEN

A bank account accrues 3% (compound) interest for 10 years. The principal is £ 20, 000. How much do you have at maturity? £ 26, 000 £ 26, 878 £ 26, 978

A smurf population falls from 240 to 200. What percentage change is that? -16. 7% -20% -24%

After tax of 20%, Kyle earns £ 5 a year. What was his earnings before tax? £ 100, 000 £ 6. 25

James Bond’s Aston Martin, originally worth £ 150, 000, depreciates by 15% each year. What is its value after 5 years? £ 66, 556 £ 67, 556 £ 68, 556

Year 9: Tax Dr J Frost (jfrost@tiffin. kingston. sch. uk)

Tax Sick. David Cameron earns £ 130, 000. The ‘Personal Allowance’ is £ 8105. If he only pays the Basic Rate of tax of 20%, how much tax does he pay. Taxable Income: £ 130, 000 - £ 8, 105 = £ 121, 895 ? 20% of £ 121, 895 = £ 24, 379 My dentist, Mr Tuthacke (see what I did there), has an annual salary of £ 48 k and can claim allowances of £ 10, 270. The lower rate of income tax is 20% and is payable on the first £ 3950 of taxable income. A basic rate of income tax is 23% and is payable on the next £ 22, 600 of taxable income. Higher rate tax is 40% is charged on any taxable income over £ 26, 550. Find the total payable tax. Taxable Income: £ 48, 000 - £ 10, 270 = £ 37, 730 20% of first £ 3950 = £ 790 £ 37, 730 - £ 3950 = £ 33780 23% of £ 22, 600 =? £ 5198 £ 33780 - £ 22, 600 = £ 11, 180 40% on rest = £ 4, 472 £ 790 + £ 5198 + £ 4472 = £ 10, 460

Tax (From the Telegraph newspaper) "Moya Greene, the Canadian chief executive of Royal Mail, was paid £ 1. 1 million, making her one of Britain’s highest paid public officials. " How much tax does she pay? Taxable Income: £ 1, 100, 000 - £ 8, 105 = £ 1, 091, 895 Taxed 50% on £ 1, 091, 895 - £ 150, 000 £ 470, 947. 50 Taxed 40% on £ 150, 000 - £ 34, 371 £ 46, 251. 60 Taxed 20% on £ 34, 370 £ 6, 874 ? Total = £ 524, 073. 10

Exercises Calculate the amount of tax paid, using the table on the right. Name Earnings Tax Paid Mr Patel £ 15, 400 £ 2, 538? Mrs Hillier £ 37, 000 Dr Palmer £ 100, 000 Prof Joglekar £ 250, 000 £ 5, 779? £ 29, 884 ? ? £ 99, 073. 10