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Simple Interest / Compound

Calculating Percentages. Int 2. Simple Interest / Compound. Compound Interest. www.mathsrevision.com. Appreciation / Depreciation. Inflation / Working back. Int 2. Starter. www.mathsrevision.com. Calculating Percentages. Int 2. Compound Interest. Appreciation More. Simple Interest.

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Simple Interest / Compound

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  1. Calculating Percentages Int 2 Simple Interest / Compound Compound Interest www.mathsrevision.com Appreciation / Depreciation Inflation / Working back created by Mr. lafferty @ www.mathsrevision.com

  2. Int 2 Starter www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  3. Calculating Percentages Int 2 Compound Interest Appreciation More Simple Interest Just Calculating Percentages www.mathsrevision.com Inflation Rising Prices Depreciation Less Working backwards created by Mr. lafferty @ www.mathsrevision.com

  4. Calculating Percentages Int 2 Learning Intention Success Criteria • To know the meaning of the term simple interest. • To understand the • term simple interest and compound interest. • To know the meaning of the term compound interest. www.mathsrevision.com 3. Know the difference between simple and compound interest. created by Mr. lafferty @ www.mathsrevision.com

  5. Calculating Percentages Just working out percentages Int 2 Simple Interest 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? www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  6. Calculating Percentages Int 2 Now try Exercise 1 Ch2 (page 8) Odd Numbers www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  7. 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. Calculating Percentages Interest calculated on new value every year Int 2 Compound Interest 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. www.mathsrevision.com Principal value created by Mr. lafferty @ www.mathsrevision.com

  8. Calculating Percentages Interest calculated on new value every year Compound Interest Int 2 Daniel has £400 in the bank. He leaves it in the bank for 3 years. The interest is 7% each year. Calculate the compoundinterest and the amount he has in the bank after 3 years. Simple Interest Y1 : Interest = 7% of £400 = £28 Amount = £400 + £28 = £428 Interest = 7% of £400 = £28 Y 2 : Interest = 7% of £428 = £29.96 3 x 28 = £84 www.mathsrevision.com Amount = £428 + £29.96 = £457.96 Y 3 : Interest = 7% of £457.96 = £32.06 Amount = £457.96 + £32.06 = £490.02 Simple Interest is only £84 Compound is £490.02 - £400 = £90.02 created by Mr. lafferty @ www.mathsrevision.com

  9. Calculating Percentages Int 2 Now try Exercise 2 Ch2 (page 8 & 9) www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  10. Int 2 Starter www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  11. Calculating Percentages Int 2 Learning Intention Success Criteria • To calculate compound interest using calculator.. • To understand how to use the calculator to calculate compound interest easier. • Show appropriate working • when solving problems. www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  12. Calculating Percentages Int 2 This is called the multiplier. Using a calculator to do Compound Formula n = period of time Days, months years www.mathsrevision.com I = initial value IMPORTANT Can only use this when percentage is fixed ± = increase or decrease V = Value created by Mr. lafferty @ www.mathsrevision.com

  13. Calculating Percentages Int 2 Using a calculator to do Compound questions Calculate the money in the bank after 3 years if the compound interest rate is 7% and the initial value is £400. n = 3 www.mathsrevision.com I =400 ± = increase 1+0.07=1.07 V= 400 x (1.07)3= £490.02 created by Mr. lafferty @ www.mathsrevision.com

  14. Calculating Percentages Int 2 Using calculator to calculate Compound questions In a jar bacteria grows 4% every hour. Initially there were 200 bacteria in the jar. How many bacteria are in the jar 4 hours later. n = 4 www.mathsrevision.com I =200 ± = increase 1+0.04=1.04 V= 200 x (1.04)4= 234 created by Mr. lafferty @ www.mathsrevision.com

  15. Calculating Percentages Int 2 Using calculator to calculate Compound questions A car reduces in price by 14% each year. Initially it cost £12 500. much is it worth 5 years later. n = 5 www.mathsrevision.com I =12 500 ± = increase 1-0.14=0.86 V= 12 500 x (0.86)5= £5880.34 created by Mr. lafferty @ www.mathsrevision.com

  16. Calculating Percentages Int 2 Now try worksheet www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  17. Int 2 Starter www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  18. Calculating Percentages Int 2 Learning Intention Success Criteria • To know the terms appreciation and depreciation. • To understand the terms appreciation and depreciation. • Show appropriate working • when solving problems containing appreciation and depreciation. www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  19. Calculating Percentages Int 2 Appreciation / Depreciation Appreciation : Going up in value e.g. House value www.mathsrevision.com Depreciation : Going down in value e.g. car value created by Mr. lafferty @ www.mathsrevision.com

  20. Quicker Method Easier 1.79 x 64995 = £116341.05 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 ? Appreciation = 79% x £ 64995 • = 0.79 x £64995 = £ 51346.05 New value = Old Value + Appreciation = £64995 + £51346.05 = £ 116341.05 Just working out percentages created by Mr. lafferty @ www.mathsrevision.com

  21. Calculating Percentages Int 2 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 www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  22. Calculating Percentages Int 2 End 2003 Depreciation = 23% x £14625 = 0.23 x £14625 = £3363.75 New value = Old value - Depreciation = £14625 - £3363.75 = £11261.25 End 2004 Depreciation = 16% x £11261.25 = 0.16 x £11261.25 = £1801.80 New Value = £11261.25 - £1801.80 = £9459.45 www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  23. Calculating Percentages Int 2 Now try MIA Ex 4 Ch2 (page 12) Odd Numbers www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  24. Int 2 Starter www.mathsrevision.com 5cm 6cm created by Mr. lafferty @ www.mathsrevision.com

  25. Calculating Percentages Int 2 Learning Intention Success Criteria • Know the term inflation. • Understand term inflation • and work out associated real-life problems. • Work out real-life problems involving inflation. www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  26. Calculating Percentages Measure of how much prices rise each year. Int 2 Inflation Inflation is normally given in percentage form and is normally in the range 0 – 10% Example 1 In 2004 a worker received a wage of £300 per week. If inflation is 2% in 2004, what should be his wage be in 2005. www.mathsrevision.com 2004 inflation = 2% 2% of £300 = £6 His wage should be £300 + £6 = £306 created by Mr. lafferty @ www.mathsrevision.com

  27. Calculating Percentages Measure of how much prices rise each year. Int 2 Inflation Inflation is normally given in percentage form and is normally in the range 0 – 10% Example 2 In 2002 a CD cost £8. The cost increases in line with inflation. What is the price in 2003 if inflation is 1.5%. www.mathsrevision.com 2002 inflation = 1.5% 1.5% of £8 = £0.12 Price is £8 + £0.12 = £8.12 created by Mr. lafferty @ www.mathsrevision.com

  28. Calculating Percentages Int 2 Now try MIA Ex 6 Ch2 (page 15) www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  29. Deduce from question : 100 % + 10 % = £88 000 We have : 110 % = £88 000 1 % : Price before is 100% : £800 x 100 = £80 000 Calculating Percentages Int 2 Reversing the change Example 1 After a 10% increase the price of a house is £88 000. What was the price before the increase. www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  30. Deduce from question : 100 % - 15 % = £2 550 We have : 85 % = £2 550 1 % : Price before is 100% : £30 x 100 = £3 000 Calculating Percentages Int 2 Reversing the change Example 2 The value of a car depreciated by 15%. It is now valued at £2550. What was it’s original price. www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

  31. Calculating Percentages Int 2 Now try MIA Ex 7 Ch2 (page 17) www.mathsrevision.com created by Mr. lafferty @ www.mathsrevision.com

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