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Guidance Notes for Teachers Some indication of content and range at level 1 and 2 is shown on the next slide. It could also be used as a single project given to students from start to finish. Relevant slides show all the diagrams/questions/answers that are required. End slides have student question sheets and a teacher question/answer sheet. End slides have printable worksheets for students. Calculator symbols are suggestions only and could be removed depending on the group. Some of the numbers in the tables have been rounded slightly to avoid complications. Use a calculator where you think necessary. Generic Advice: The preparation below is advisable in the majority of presentations. 1.Print off the teacher question and answer sheets/worksheets 2.Print off the student question sheets/worksheets 3.Run through the presentation yourself answering the questions 4.Decide how you are going to deliver the presentation. (a) Are you going to go through it from start to finish with the class, perhaps using it as an example/demonstration of functional maths and focusing on the development of the processing skills involved at each stage? (b) Are you going to use only part of the presentation? (c) Are you simply going to use the presentation to introduce the activity and let the class work on their own through the question sheets but refer to some of the elements/answers within the presentation when needed? 5.Remember the slides are editable so if you wish to introduce an open question/small investigation of your own then simply choose the relevant slide add/delete your own text (using a text box if needed).

Content and Skills Coverage and range: Level 1 Understand and use whole numbers and recognise negative numbers in practical contexts Add, subtract, multiply and divide using a range of mental methods Multiply and divide whole numbers by 10 and 100 using mental arithmetic Understand and use equivalences between common fractions, decimals and percentages Add and subtract decimal up to two decimal places Solve simple problems involving ratio, where one number is a multiple of the other Use simple formulae expressed in words for one- or two-step operations Solve problems requiring calculation with common measures including money, time, length, weight, capacity and temperature Convert units of measure in the same system Work out areas, perimeters and volumes in practical situations Construct models and draw shapes, measuring and drawing angles and identifying line symmetry Extract and interpret information from tables, diagrams, charts and graphs Collect and record discrete data and organise and represent information in different ways Find mean and range Use probability to show that some events are more likely to occur than others Understand outcomes, check calculations and explain results Understand and use positive and negative numbers of any size in practical contexts Carry out calculations with numbers of any size in practical contexts Understand, use and calculate ratio and proportion, including problems involving scale Understand and use equivalences between fractions, decimals and percentages Add and subtract fractions; add, subtract, multiply and divide decimals to a given number of decimal places Understand and use simple equations and simple formulae involving one- or two-step operations Recognise and use 2D representations of 3D objects. Find area, perimeter and volume of common shapes Use, convert and calculate using metric and, where appropriate, imperial measures Collect and represent discrete and continuous data, using ICT where appropriate Use and interpret statistical measures, tables and diagrams, for discrete and continuous data using ICT where appropriate Use statistical methods to investigate situations Use a numerical scale from 0 to 1 to express and compare probabilities Title: Mortgages Content and skills covered Coverage and range: Level 2 At least 1 from each area

Intro

A Mortgage is a loan, normally given by a bank or building society to enable someone to purchase a house/flat/apartment etc. The loan is often for a very large amount of money and so it usually has to be paid back over many years otherwise it would not be affordable for most people. As an example a typical first time buyer may borrow £125,000 over a 25 year period. During this period all the money borrowed (capital) must be paid back together with interest on the loan. The loan is secured against the property purchased. This means that if the borrower can no longer afford the payments then the lender may repossess the property and sell it so that they can get their money back.

Mortgages Types LoanTerm Interest Rate Interest To Pay Total To Pay Monthly Repayment £125,00025 years5%£94,220£219,000£730 Repayment Mortgage LoanTerm Interest Rate Interest To Pay Total To Pay Monthly Repayment £125,00025 years5%£156,250£ £520 After Amount Owed Interest Paid 5 Years £110,725 £29, Years £92,405 £55, Years £68,894 £75, Years £38,721 £89, Years £0 £94,220 Interest Only Mortgage After Amount. Owed Interest Paid 5 Years £125,000 £31, Years £125,000 £62, Years £125,000 £93, Years £125,000 £125, Years £125,000 £156,250 With a repayment mortgage, part of the loan (capital) and part of the interest are paid off each month. At the end of the period (25 years in this case), the loan and interest have been paid. There is nothing more to pay. With an interest only mortgage the monthly repayments pay off only the interest owed (which is higher) and none of the capital. Discuss the advantages and disadvantages of these two types of mortgage.

Repayment Mortgages LoanTerm Interest Rate Interest To Pay Total To Pay Monthly Repayment £100,00015 years4%£33,200£133,200£740 £100,00020 years4%£45,440£145,440£606 £100,00025 years4%£58,400£158,400£528 Repayment mortgages are by far the most common type of mortgage. The table above shows some information on a £100,000 loan at a 4% interest rate to be paid back over different time periods. Question 1. What is the difference in monthly repayments for 20 and the 25 year periods? £78 Question 2. How much more interest is paid on the 25 year mortgage than on the 15 year mortgage? £25,200 Question 3. After a few years some people earn more money through pay rises/promotion etc and they like to increase their monthly repayments. Why do you think this might be? The mortgage will be paid off quicker with less interest. Question 4. Using a calculator, show for each case above, that balance will be zero at the end of the term. The first one is done for you: £740 x 12 x 15 = £133,200

Repayment Mortgages LoanTerm Interest Rate Interest To Pay Total To Pay Monthly Repayment £200,00025 years4%£116,800£316,800£1,056 £200,00025 years5%£151,000£351,000£1,170 £200,00025 years6%£187,000£387,000£1,290 £200,00025 years7%£223,900£423,900£1,395 £200,00025 years8%£263,200£463,200£1,544 7 and 8% Question 8. For which interest rates does the interest to be paid exceed the original loan amount? £488 Question 6. How much more would the monthly repayments be at the 8% rate rather than the 4% rate? £107,100 Question 7. How much more interest would you pay at the 7% rate rather than the 4% rate? The table above shows some information on a £200,000 mortgage paid back over 25 years at different interest rates. Many people have variable rate mortgages which means that the interest rate can change at any time within the period of the loan. The rate is usually linked to and affected by, the Bank of England base rate. This can, in certain circumstances, fluctuate wildly. Question 5. Discuss the advantages/disadvantages of having a variable rate mortgage.

Repayment Mortgages LoanTerm Interest Rate Interest To Pay Total To Pay Monthly Repayment £200,00025 years4%£116,800£316,800£1,056 £200,00025 years5%£151,000£351,000£1,170 £200,00025 years6%£187,000£387,000£1,290 £200,00025 years7%£223,900£423,900£1,395 £200,00025 years8%£263,200£463,200£1,544 The table above shows some information on a £200,000 mortgage paid back over 25 years at different interest rates. Many people have variable rate mortgages which means that the interest rate can change at any time within the period of the loan. The rate is usually linked to and affected by the Bank of England base rate. This can in certain circumstances, fluctuate wildly. Question 9. Would you expect a 9% interest rate to make the total repayments greater than ½ a million pounds? Yes (£503,000 in fact) Question 10. One of the monthly repayments shown above is incorrect. Use a calculator to help you find which one. £ 1395 (should be £1413).

Repayment Mortgages LoanTerm Interest Rate Interest To Pay Total To Pay Monthly Repayment £200,00025 years4%£116,800£316,800£1,056 £200,00025 years5%£151,000£351,000£1,170 £200,00025 years6%£187,000£387,000£1,290 £200,00025 years7%£223,900£423,900£1,413 £200,00025 years8%£263,200£463,200£1,544 It is possible to have a fixed rate mortgage rather than a variable rate. This is normally allowed by the lender in the earlier years of the mortgage and the interest rate is usually fixed for a limited period of between 1 and 5 years. When it comes to an end the lender will switch you back to the variable rate or possibly offer you another fixed rate one. Question 11. Discuss the advantages/disadvantages of having a fixed rate mortgage as compared to a variable rate. Question 12. What is the median “interest to pay” for the table above? £ 187,000

Repayment Mortgages £120,000£130,000£140,000£150,000£160, years£949£1,028£1,107£1,186£1, years£792£858£924£990£1, years£702£760£818£876£ years£644£698£752£806£860 The table shows monthly repayments for an interest rate of 5% (with some rounding). Question 13. Sara and Steve are paying back a £120,000 mortgage over 15 years. Suman and Raul are paying back a £150,000 mortgage over 25 years. What is the difference in their monthly repayments? £73 Question 15. Robert and his wife have a 25 year mortgage and they are paying £58 a month more than their next door neighbours who also have a 25 Year mortgage. Can you tell from the table how much their mortgage is? No (all repayments differ by £58) Question 16. Use the information in the table to calculate the monthly repayment on a £250,000 mortgage over 30 years. £644 + £698 = £1342 Question 14. Calculate the total repayments for Asif and Shreeva who have a 20 year, £140,000 mortgage. £221,760 Question 17. Calculate the mean and range of the monthly repayments for the £140,000 mortgages. (nearest £). Mean = £900, range = £355

Repayment Mortgages IanBeckyChrisDanielleEricFalon Incomes£24,000£12,000£15,000£29,000£35,000£25,000 The three couples below are thinking about buying their first house and visit the local building society to see how much they will be able to borrow. The Building Society will offer couples a loan equivalent to 2½ times their joint salary. They also normally insist that a couple have a 25% deposit to put down on any property that they buy. Question 18. Using the information on their incomes, calculate the loans that each couple may possibly be offered. 2½ x £36,000 = £90,0002½ x £44,000 = £110,0002½ x £60,000 = £150,000 Question 19. Eric and Falon hope to buy a £180,000 property. Will they be able afford it? Yes, since they need a £45,000 deposit which they have and £180,000- £45,000 = £135,000 which is less than the loan offer of £150,000. Savings £20,000None£50,000 Question 20. How much more do Ian and Becky need to save, in order to purchase a £100,000 property? £5,000

Worksheet 1 LoanTerm Interest Rate Interest To Pay Total To Pay Monthly Repayment £100,00015 years4%£33,200£133,200£740 £100,00020 years4%£45,400£145,400£606 £100,00025 years4%£58,400£158,400£528 Worksheet for Questions LoanTerm Interest Rate Interest To Pay Total To Pay Monthly Repayment £200,00025 years4%£116,800£316,800£1,056 £200,00025 years5%£151,000£351,000£1,170 £200,00025 years6%£187,000£387,000£1,290 £200,00025 years7%£223,900£423,900£1,395 £200,00025 years8%£263,200£463,200£1,544 Worksheet for Questions LoanTerm Interest Rate Interest To Pay Total To Pay Monthly Repayment £200,00025 years4%£116,800£316,800£1,056 £200,00025 years5%£151,000£351,000£1,170 £200,00025 years6%£187,000£387,000£1,290 £200,00025 years7%£223,900£423,900£1,395 £200,00025 years8%£263,200£463,200£1,544 Worksheet for Questions

£120,000£130,000£140,000£150,000£160, years£949£1,028£1,107£1,186£1, years£792£858£924£990£1, years£702£760£818£876£ years£644£698£752£806£860 Worksheet for Questions IanBeckyChrisDanielleEricFalon Incomes£24,000£12,000£15,000£29,000£35,000£25,000 Savings£20,000None£50,000 Worksheet for Questions Worksheet 2

Teacher Q + A (1) Question 1. What is the difference in monthly repayments for 20 and the 25 year periods? £78 Question 2. How much more interest is paid on the 25 year mortgage than on the 15 year mortgage? £25,200 Question 3. After a few years some people earn more money through pay rises/promotion etc and they like to increase their monthly repayments. Why do you think this might be? 7 and 8% Question 8. For which interest rates does the interest to be paid exceed the original loan amount? £488 Question 6. How much more would the monthly repayments be at the 8% rate rather than the 4% rate? £107,100 Question 7. How much more interest would you pay at the 7% rate rather than the 4% rate? Question 5. Discuss the advantages/disadvantages of having a variable rate mortgage. Question 9. Would you expect a 9% interest rate to make the total repayments greater than ½ a million pounds? Yes (£503,000 in fact) Question 10. One of the monthly repayments shown above is incorrect. Use a calculator to help you find which one. £ 1395 (should be £1413). Teacher Q + A (1) The mortgage will be paid off quicker with less interest. Question 4. Using a calculator, show for each case above that balance will be zero at the end of the term. The first one is done for you: £740 x 12 x 15 = £133,200

Teacher Q + A (2) Question 11. Discuss the advantages/disadvantages of having a fixed rate mortgage as compared to a variable rate. Question 12. What is the median “interest to pay” for the table above? £ 187,000 Question 13. Sara and Steve are paying back a £120,000 mortgage over 15 years. Suman and Raul are paying back a £150,000 mortgage over 25 years. What is the difference in their monthly repayments? £73 Question 15. Robert and his wife have a 25 year mortgage and they are paying £58 a month more than their next door neighbours who also have a 25 Year mortgage. Can you tell from the table how much their mortgage is? No (all repayments differ by £58) Question 16. Use the information in the table to calculate the monthly repayment on a £250,000 mortgage over 30 years. £644 + £698 = £1342 Question 14. Calculate the total repayments for Asif and Shreeva who have a 20 year, £140,000 mortgage. £221,760 Question 17. Calculate the mean and range of the monthly repayments for the £140,000 mortgages. (nearest £). Mean = £900, range = £355 Question 18. Using the information on their incomes, calculate the loans that each couple may possibly be offered. 2½ x £36,000 = £90,0002½ x £44,000 = £110,0002½ x £60,000 = £150,000 Question 19. Eric and Falon hope to buy a £180,000 property. Will they be able afford it? Yes, since they need a £45,000 deposit which they have and £180,000-£45,000 = £135,000 which is less than the loan offer of £150,000. Question 20. How much more do Ian and Becky need to save, in order to purchase a £100,000 property? £5,000 Teacher Q + A (1)

Student Q 1 Question 1. What is the difference in monthly repayments for 20 and the 25 year periods? Question 2. How much more interest is paid on the 25 year mortgage than on the 15 year mortgage? Question 3. After a few years some people earn more money through pay rises/promotion etc and they like to increase their monthly repayments. Why do you think this might be? Question 4. Using a calculator, show for each case above that balance will be zero at the end of the term. The first one is done for you: £740 x 12 x 15 = £133,200 Question 8. For which interest rates does the interest to be paid exceed the original loan amount? Question 6. How much more would the monthly repayments be at the 8% rate rather than the 4% rate? Question 7. How much more interest would you pay at the 7% rate rather than the 4% rate? Question 5. Discuss the advantages/disadvantages of having a variable rate mortgage. Question 9. Would you expect a 9% interest rate to make the total repayments greater than ½ a million pounds? Question 10. One of the monthly repayments shown above is incorrect. Use a calculator to help you find which one. Student Question Sheet 1

Student Q2 Question 11. Discuss the advantages/disadvantages of having a fixed rate mortgage as compared to a variable rate. Question 12. What is the median “interest to pay” for the table above? Question 13. Sara and Steve are paying back a £120,000 mortgage over 15 years. Suman and Raul are paying back a £150,000 mortgage over 25 years. What is the difference in their monthly repayments? Question 15. Robert and his wife have a 25 year mortgage and they are paying £58 a month more than their next door neighbours who also have a 25 Year mortgage. Can you tell from the table how much their mortgage is? Question 16. Use the information in the table to calculate the monthly repayment on a £250,000 mortgage over 30 years. Question 14. Calculate the total repayments for Asif and Shreeva who have a 20 year, £140,000 mortgage. Question 17. Calculate the mean and range of the monthly repayments for the £140,000 mortgages. (nearest £). Question 18. Using the information on their incomes, calculate the loans that each couple may possibly be offered. Question 19. Eric and Falon hope to buy a £180,000 property. Will they be able afford it? Question 20. How much more do Ian and Becky need to save, in order to purchase a £100,000 property? Student Question Sheet 1