S4_3_Credit_Money_Chapter_2

S4_3_Credit_Money_Chapter_2 - Money S4 Credit Wages &...

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Unformatted text preview: Money S4 Credit Wages & Salaries National Insurance Income Tax Banks & Building Societies Savings and Interest Compound Interest Appreciation & Depreciation Working Backwards www.mathsrevision.com Wages Rises Time-Sheets Overtime Pay Piecework & Commission Payslip Starter Questions S4 Credit Q1. www.mathsrevision.com Q2. Q3. Factorise 2x 2 - 3x - 2 Write down the probability of picking out a number greater than 7 in the national lottery. If a = 2 and b = 1 calculate 4a2 3b2 Q4. Calculate Monday 13 February 2012 2 1 2 +3 3 6 Wages & Salaries S4 Credit Learning Intention Success Criteria 1. Understand the term weekly monthly and annual salary. 2. Calculate weekly, monthly and annual salary. www.mathsrevision.com 1. To explain how to work out weekly, monthly and annual salary / wage. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Wages & Salaries S4 Credit www.mathsrevision.com Annual Wage / Salary How much a person is paid in a year 12 months in a year 52 weeks in a year 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Wages & Salaries S4 Credit Example 1 : www.mathsrevision.com A shop assistant gets paid 12 428 a year. How much is her weekly wage. Weekly wage = 12 428 52 = 239 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Wages & Salaries S4 Credit Example 2 : www.mathsrevision.com A mechanic gets paid 1 100 a month. A bus driver gets paid 260 a week. Who gets the better annual salary. Mechanic : Bus Driver : 13 Feb 2012 Annual Salary = 1 100 x 12 = 13 200 Annual Salary = 260 x 52 = 13 520 Bus driver has better annual wage Created by Mr. Lafferty Maths Dept. Wages & Salaries S4 Credit Example 3 : www.mathsrevision.com Jim is a joiner his hourly rate of pay is 10.50. He works 40 hours a week. What is his basic weekly pay? What is his annual salary? Weekly Pay is = 10.50 x 40 = 420 Annual Salary = 420 x 52 = 21 840 Wages & Salaries S4 Credit Example 4 : www.mathsrevision.com Daryl gets an annual salary of 30 000. What is his monthly wage. What is his weekly wage. Monthly wage: 30 000 12 = 2 500 Weekly wage : 30 000 52 = 576.92 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Wages & Salaries S4 Credit www.mathsrevision.com Now try Ex 3.1 Ch 2 (page 27) Odd questions 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions S4 Credit Q1. www.mathsrevision.com Q2. Q3. Find the roots for the quadratic to 1 decimal place x 2 + 11x + 1 = 0 Write down the probability of picking out a number greater than 20 in the national lottery. If a = 3 then find f(a) f(a) = 2a3 Q4. Does 36 4 0 = 1.4 4 10 3 Monday 13 February 2012 Wages Rises S4 Credit Learning Intention Success Criteria 1. Calculate a percentage rise. 2. Calculate new wages after a percentage rise. www.mathsrevision.com 1. To explain how to work out new wages after a wage rise. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Wages Rises S4 Credit Example 1 : www.mathsrevision.com Gerry earned an annual salary of 18 000 last year. He receives a 4% rise this year. What is his new salary. Rise : 4 100 x 18 000 = 720 New salary : 13 Feb 2012 18 000 + 720 = 18 720 Created by Mr. Lafferty Maths Dept. Wages Rises S4 Credit Example 2 : www.mathsrevision.com Amanda new weekly wage after a 5% pay rise , is 363.93 Calculate her wage before the rise. 100% + 5% = 105% 105% = 363.93 100% = 363.93 105 x 100 = 346.60 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Wages Rises S4 Credit www.mathsrevision.com Now try Ex 3.2 Ch 2 (page 28) Odd questions 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions S4 Credit Q1. www.mathsrevision.com Find the roots of the quadratic to 1 decimal place 5 -x -7x Q2. Q3. Q4. 2 =0 Write down the probability of picking out a number greater than 33 in the national lottery. If f(x) = (x + 1)(x 2) find f(1) Explain why the line y + 3x 6 = 0 cut the xaxis at (2,0) . Monday 13 February 2012 S4 Credit Timesheet Learning Intention Success Criteria 1. Calculate hours worked. 1. To work out hours worked from a time sheet using the counting method. www.mathsrevision.com 13 Feb 2012 Created by Mr. Lafferty Maths Dept. S4 Credit Timesheet Name : Joe Bloggs Employee No. 12345 Out 1200 1200 1230 1300 1230 In 1300 1330 1300 1400 1400 Out 1700 1730 1630 1700 1630 Total Week10 In Mon Tue Wed Thurs Fri 0800 0800 0830 0800 0800 Total hours worked 8 8 7.5 8 7 38.5 www.mathsrevision.com 13 Feb 2012 Created by Mr. Lafferty Maths Dept. S4 Credit Timesheet Example 1 : Frances starts work at 7.30am and finishes at 3pm. How many hours did she work. 30mins 7.30am 8.00am 7 hours 3pm www.mathsrevision.com Total 30mins + 7hours = 7hours 30 mins 13 Feb 2012 Created by Mr. Lafferty Maths Dept. S4 Credit Timesheet Example2 : Rachel hourly rate is 6.50. How much is her weekly wage. Weekly wage = 38.5 x 6.50 = 250.25 www.mathsrevision.com 13 Feb 2012 Created by Mr. Lafferty Maths Dept. S4 Credit Timesheet Now try Ex 4.1 Ch 2 (page 30) Odd questions www.mathsrevision.com 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions S4 Credit Q1. www.mathsrevision.com Q2. Q3. Solve the equation to 1 decimal place x 2 -7x -2 = 0 Write down the probability of picking out a number greater than 49 in the national lottery. Factorise 9m2 25n2 Q4. Monday 13 February 2012 Where does the line 2y 6x + 8 =0 cut yaxis. Overtime Pay S4 Credit Learning Intention Success Criteria 1. Understand the terms overtime, `double time' and `time and a half'. 2. Calculate wages with overtime. www.mathsrevision.com 1. To explain how to work out wages which include overtime rates. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Overtime Pay S4 Credit Overtime : When you do extra work above your basic You get a better hourly rate for overtime. Write down the two common rates of overtime hours. www.mathsrevision.com Double time (x2) Time and a half (x1.5) Overtime Pay S4 Credit www.mathsrevision.com Example 1 : Anthony the painter works for 6.00 per hour. His overtime rate is "Double time". What does he get paid for 4 hours overtime. 4 hours Overtime is = 13 Feb 2012 4 x 6 x 2 = 48.00 Created by Mr. Lafferty Maths Dept. Overtime Pay S4 Credit www.mathsrevision.com Example 2 : John the gardener works a basic 40 hours a week. He does 5 hours overtime at `double time' on Saturday. His hourly rate is 8 per hour. Work out his overtime pay and then his total pay. 5 hours overtime is = 40 hours basic time is = 5 x 8 x 2 = 80.00 40 x 8 = 320.00 Total pay is = 320 + 80 = 400 Overtime Pay S4 Credit www.mathsrevision.com Now try Ex 4.2 Ch 2 (page 31) Even questions 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions S4 Credit Q1. www.mathsrevision.com Find the roots to 1 decimal place 4 -7x +x Q2. 2 =0 A sofa is reduced by 20% to 300 in a sale. Is the original price 360. Q3. Calculate 3 1 3 -1 10 3 Monday 13 February 2012 Commission S4 Credit Learning Intention Success Criteria 1. Understand the term commission. 2. Calculate wages involving commission. www.mathsrevision.com 1. To explain how to work out wages when commission is involved. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Commission S4 Credit www.mathsrevision.com Commission : Money earned based on how much you sell. Usual expressed as a percentage. Write some people who get commission Car sales person Double glazing sales person Commission S4 Credit Example 1 : www.mathsrevision.com Anthony does maths tuition and charges 12.50. (a) How much does he earn in a week if he does 9 lesson. (b) How much for a course of 20 lessons. (a) (b) 12.50 x 9 = 112.50 12.50 x 20 = 250 Commission S4 Credit Example 2 : www.mathsrevision.com Sean sells cars. He is paid a commission of 5% on any cars he sells. Last week he sold 20 000 worth of cars. How much commission was he paid ? Commission : 5 100 x 20 000 = 1 000 Commission S4 Credit www.mathsrevision.com Now try Ex 5.1 Ch 2 (page 32) Odd questions 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions S4 Credit Q1. www.mathsrevision.com Q2. Q3. Find the roots to 1 decimal place 3x 2 - 8x -2 = 0 A house has increase by 10% to 77 000 in a year. Find the price before the increase. Find the gradient and where the line y +4x 3 =0 cuts the xaxis. Q4. Calculate 7 3 1 - 9 8 Monday 13 February 2012 Payslips S4 Credit Learning Intention Success Criteria 1. Understand the terms Gross, Deductions and NET pay. 2. Calculate NET pay. www.mathsrevision.com 1. To explain how to work out NET pay. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Payslips S4 Credit Write down some Gross Pay : : : What you are paid by the employer. Taken off your wages. Your take home pay. www.mathsrevision.com Deductions Net Pay Tax Pension National Insurance Payslips S4 Credit www.mathsrevision.com Example 1 : Calculate the Net wage for the following : Gross 15 550 13 025 22 430 Deductions 3 400 2 905 5 094 Net Wage 12 150 10 120 17 336 Payslips S4 Credit www.mathsrevision.com Example 2 : Calculate the Net wage for this payslip : Name : Bill Smit h I ncome Basic 650. 00 O/ T 54. 00 25. 00 Bonus Pension 22. 00 Tot al Tot al NET PAY Deduct ions Tax 102. 00 Nat I ns. 704.00 149.00 555.00 Payslips S4 Credit www.mathsrevision.com Example 3 : Calculate the Net wage for this payslip : Name : J oe Bloggs I ncome Basic 603. 65 O/ T 85. 50 30. 72 Bonus Pension 50. 00 34. 29 Tot al Tot al NET PAY Deduct ions Tax 142. 75 Nat I ns. 739.15 207.76 531.39 Payslips S4 Credit www.mathsrevision.com Now try Ex 6.1 Ch 2 (page 33) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions S4 Credit Q1. www.mathsrevision.com Find the standard deviation for the data below 6, 5 , 3 , 1, 5 Q2. Solve the equation 2 sin x o + 1 = 0 0 < x < 180 Monday 13 February 2012 S4 Credit National Insurance Contributions Learning Intention Success Criteria 1. Understand the terms Gross, Deductions and NET pay. 2. Calculate NET pay. www.mathsrevision.com 1. To explain how to work out NET pay. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. S4 Credit National Insurance Contributions This is a government tax on earnings intended to contribute towards .......... Do you know the rest ! www.mathsrevision.com unemployment State Pension illhealth S4 Credit National Insurance Contributions Rates for 2004 / 05 www.mathsrevision.com Rate 0% 11% 1% Weekly < 91 91 610 > 610 Annual < 4745 4745 31 720 > 31 720 S4 Credit National Insurance Contributions Rate Weekly < 91 91 610 > 610 Annual < 4745 4745 31 720 > 31 720 0% 11% 1% www.mathsrevision.com Calculate how much Kylo will pay in NIC if he earns 400 a week. He has to pay NIC on 11% of 309 400 91 = 309 33.99 = 11 100 x 309 = S4 Credit Rate 0% 11% 1% National Insurance Contributions Weekly < 91 91 610 > 610 < 4745 Annual www.mathsrevision.com 4745 31 720 > 31 720 Charlotte earns 1000 a week. How much NIC will she pay per week. She has to pay NIC on 610 91 = 519 @ 11% 1000 610 = 390 @ 1% 60.99 (11 100 x 519) + (1 100 x 390) = S4 Credit National Insurance Contributions Now try Ex 7.1 Ch 2 (page 35) www.mathsrevision.com 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions S4 Credit Q1. www.mathsrevision.com Find the standard deviation for the data below 2, 4 , 3 , 1, 2 Q2. Solve the equation 2 cos x o + 3 = 0 0 < x < 360 Monday 13 February 2012 Income Tax S4 Credit Learning Intention Success Criteria 1. Understand the term Income Tax. 2. Calculate Income Tax for a given salary. www.mathsrevision.com 1. To explain how to work out Income Tax calculations. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Income Tax S4 Credit www.mathsrevision.com If your income in a tax year is below a certain value you do not pay tax. The tax allowance is made up of a personal allowance plus other special allowances. equipment Membership of professional bodies Special clothing Income Tax S4 Credit Taxable Rates for 2004 / 05 www.mathsrevision.com Taxable income Up to 4745 0 2020 2020 31 400 Over 31 400 Rate of Tax 0% 10% 22% 40% Taxable income Up to 4745 S4 Credit 0 2020 Income Tax Rate of Tax 0% 10% 22% 40% 2020 31 400 Over 31 400 www.mathsrevision.com Calculate David's income tax if he earns 27 000 a year. Personal allowance 4745 Taxable Income 27 000 4745 = 22 255 Tax @ 10% = 10% of 2020 = 202 Tax @ 22% = 22% of ( 22 255 2020) = 22% of 20 235 = 4451.70 Total Income tax = 202 + 4451.70 = 4653.70 Taxable income Up to 4745 S4 Credit 0 2020 Income Tax Rate of Tax 0% 10% 22% 40% 2020 31 400 Over 31 400 www.mathsrevision.com Lauren, a successful business woman earns 70 000. What is her total tax paid and her income after tax. Personal allowance 4745 Taxable Income 70 000 4745 = 65 255 Tax @ 10% = 10% of 2020 = 202 Tax @ 22% = 22% of ( 31 400 2020) = 6463.60 Tax @ 40% = 40% of ( 65 255 31 400) = 13 542 Total tax = 202 + 6463.60 + 13 542 = 20 207.60 Taxable income Up to 4745 S4 Credit 0 2020 Income Tax Rate of Tax 0% 10% 22% 40% 20 207.60 2020 31 400 Over 31 400 www.mathsrevision.com Total tax = 202 + 6463.60 + 13 542 = Income after tax = 70 000 20 207.60 = 49 792.40 Income Tax S4 Credit www.mathsrevision.com Now try Ex 8.1 & 8.2 Ch 2 (page 37) Even Numbers Only 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions S4 Credit Q1. www.mathsrevision.com Find the standard deviation for the data below 2, 4 , 3 , 1, 2 Q2. Find the coordinates where the line and curve meet. Monday 13 February 2012 Banks & Building Societies S4 Credit Learning Intention Success Criteria 1. Understand the main services from a bank account. 2. Interpret bank statements. www.mathsrevision.com 1. To explain how bank accounts work. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Banks & Building Societies S4 Credit Banks and Building Societies help us manage our money. www.mathsrevision.com What might we get if we open an account at a bank ? DR = overdrawn Cheque book Cash Card Credit Card Banks & Building Societies S4 Credit Copy and complete the bank statement www.mathsrevision.com 61.03 33.46 DR 590.62 Banks & Building Societies S4 Credit www.mathsrevision.com Now try Ex 9.1 Ch 2 (page 40) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions S4 Credit Q1. www.mathsrevision.com A line passes through the points ( 3, 8) and ( 5,10) (a) (b) Find the gradient. Where does the line cross the x and y axis. x 2y = 10 2x + y = 20 Q2. Solve Monday 13 February 2012 Savings & Interest S4 Credit Learning Intention Success Criteria 1. To know the meaning of the term simple interest. 2. To know the meaning of the term compound interest. 3. Know the difference between simple and compound interest. www.mathsrevision.com 1. To understand the term simple interest and compound interest. Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 61 Savings & Interest S4 Credit Just working out percentages Simple Interest www.mathsrevision.com I have 400 in the Bank. At the end of each year I receive 7% of 400 in interest. How much interest do I receive after 3 years. How much do I now have? I nt erest = 7 100 400 = 28 Af t er 3 years int erest is 3 x 28 = 84. Tot al in bank is = 400 + 84 = 484 Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 62 Savings & Interest S4 Credit Now try Ex 10.1 www.mathsrevision.com Ch2 (page 41) Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 63 Starter Questions S4 Credit Q1. www.mathsrevision.com Find the standard deviation for the data below 10 , 4 , 10 , 1, 5 Q2. Find the coordinates where the line and curve meet. Monday 13 February 2012 Compound Interest S4 Credit Learning Intention Success Criteria 1. To know when to use compound formula. 2. Solve problems involving compound formula. www.mathsrevision.com 1. To show how to use the compound formula for appropriate problems. Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 65 S4 Credit Interest calculated on new value every year Compound Interest www.mathsrevision.com Real life Interest is not a fixed quantity year after year. One year's interest becomes part of the next year's amount. Each year's interest is calculated on the amount at the start of the year. Principal value Example Daniel has 400 in the bank. He leaves it in the bank for 3 years. The interest is 7% each year. Calculate the simply interest and then the compound interest after 3 years. Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 66 Compound Interest S4 Credit Interest calculated on new value every year www.mathsrevision.com Daniel has 400 in the bank. He leaves it in the bank for 3 years. The interest is 7% each year. Calculate the compound interest and the amount he has in the bank after 3 years. Simple Interest Interest = 7% of 400 = 28 3 x 28 = 84 Y1 : Interest = 7% of 400 = 28 Amount = 400 + 28 = 428 Y 2 : Interest = 7% of 428 = 29.96 Amount = 428 + 29.96 = 457.96 Y 3 : Interest = 7% of 457.96 = 32.06 Amount = 457.06 + 32.06 = 490.02 Simple Interest is only 84 Monday, February 13, 2012 Compound is 490.02 400 = 90.02 created by Mr. lafferty @ www.mathsrevision.com 67 Compound Interest S4 Credit Easier Method This is called the multiplier. n www.mathsrevision.com % V = I1 100 n = period of time Days, months years I = initial value = increase or decrease V = Value 68 IMPORTANT Can only use this when percentage is fixed Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com Compound Interest S4 Credit Calculate the money in the bank after 3 years if the compound interest rate is 7% and the initial value is 400. www.mathsrevision.com % V = I1 100 3 n n = 3 I =400 = increase 1+0.07=1.07 V= 400 x (1.07) = 490.02 Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 69 Compound Interest S4 Credit www.mathsrevision.com Now try Ex 10.2 Ch2 (page 43) Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 70 Starter Questions S4 Credit Q1. www.mathsrevision.com Solve the equations x + 4y = 0 2x - y = 9 Q2. Find the coordinates where the line and curve meet. Monday 13 February 2012 Appreciation & Depreciation S4 Credit Learning Intention Success Criteria 1. To know the terms appreciation and depreciation. 2. Show appropriate working when solving problems containing appreciation and depreciation. www.mathsrevision.com 1. To understand the terms appreciation and depreciation. Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 72 Appreciation & Depreciation S4 Credit www.mathsrevision.com Appreciation : Going up in value e.g. House value Depreciation : Going down in value e.g. car value Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 73 Quicker Method Easier S4 Credit Average house price in Ayr has appreciated by 79% over past 10 years. If you bought the house for 64995 in 1994 how much would the house be worth now ? 1.79 x 64995 = 116341.05 Appreciation = 79% x 64995 = 0.79 x 64995 = 51346.05 New value = Old Value + Appreciation = 64995 + 51346.05 = 116341.05 Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com Just working out percentages 74 Appreciation & Depreciation S4 Credit A Mini Cooper cost 14 625 in 2002 At the end 2003 it depreciated by 23% At the end 2004 it will depreciate by a further 16% What will the mini cooper worth at end 2004? End 2003 Depreciation = 23% x 14625 = 0.23 x 14625 = 3363.75 New value = Old value Depreciation = 14625 3363.75 = 11261.25 Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com www.mathsrevision.com 75 Appreciation & Depreciation S4 Credit End 2003 Depreciation www.mathsrevision.com New value End 2004 Depreciation = 23% x 14625 = 0.23 x 14625 = 3363.75 = Old value Depreciation = 14625 3363.75 = 11261.25 = 16% x 11261.25 = 0.16 x 11261.25 = 1801.80 = 11261.25 1801.80 = 9459.45 New Value Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 76 Appreciation & Depreciation S4 Credit www.mathsrevision.com Now try MIA Ex 11.1 Ch2 (page 45) Odd Numbers Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 77 Starter Questions S4 Credit Q1. www.mathsrevision.com Solve the equations 2x + 3 y = 6 3x - 3 y = 19 Q2. Solve the coordinates where the line and curve meet. Monday 13 February 2012 Work Backwards S4 Credit Learning Intention Success Criteria 1. To understand the process of work backwards. 2. Solve problems using backwards process. www.mathsrevision.com 1. To understand how to work backwards to find original price. Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 79 Work Backwards S4 Credit Example 1 www.mathsrevision.com After a 10% increase the price of a house is 88 000. What was the price before the increase. Deduce from question : We have : 100 % + 10 % = 88 000 110 % = 88 000 1 % : 88 000 Price before is 100% : Monday, February 13, 2012 110 = 800 800 x 100 = 80 000 80 created by Mr. lafferty @ www.mathsrevision.com Work Backwards S4 Credit Example 2 www.mathsrevision.com The value of a car depreciated by 15%. It is now valued at 2550. What was it's original price. Deduce from question : We have : 1 % : Price before is 100% : Monday, February 13, 2012 100 % - 15 % = 2 550 85 % = 2 550 2 550 85 = 30 30 x 100 = 3 000 81 created by Mr. lafferty @ www.mathsrevision.com Work Backwards S4 Credit www.mathsrevision.com Now try MIA Ex 11.2 Ch2 (page 46) Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 82 ...
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This note was uploaded on 02/13/2012 for the course MAT 1117 MAT 117 taught by Professor White during the Spring '09 term at University of Phoenix.

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