Simple Interest / Compound

1. Calculating Percentages Int 2 Simple Interest / Compound Compound Interest Appreciation / Depreciation Inflation / Working back

2. Int 2 Starter

3. Calculating Percentages Int 2 Compound Interest Appreciation More Simple Interest Just Calculating Percentages Inflation Rising Prices Depreciation Less Working backwards

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. 3. Know the difference between simple and compound interest.

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?

6. Calculating Percentages Int 2 Now try Exercise 1 Ch2 (page 8) Odd Numbers

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 compound interest and the amount he has in the bank 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. Principal value

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 compound interest and the amount he has in the bank after 3 years. Year 1 : Interest = 7% of £400 = £28 Amount = £400 + £28 = £428 Year 2 : Interest = 7% of £428 = £29.96 Amount = £428 + £29.96 = £457.96 Year 3 : Interest = 7% of £457.96 = £32.06 Amount = £457.96 + £32.06 = £490.02 Compound interest is £490.02 - £400 = £90.02

9. Calculating Percentages Int 2 Now try Exercise 2 Ch2 (page 9 & 10)

10. Int 2 Starter

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.

12. Calculating Percentages This is called the multiplier. Int 2 Using calculator to calculate Compound Calculate the compound interest on £400 over 3 years if interest rate is 7%. Year 1 : Total = 107% of £400 = 1.07 x £400 Year 2 : it is worth 107% of (1.07 x £400) = 1.07 x 1.07 x £400 = (1.07)2 x £400 Year 3 : it is worth 107% of (1.072) x £400 = 1.07 x 1.07 x 1.07 x £400 = (1.07)3 x £400 = £490.02

13. Int 2 Starter

14. 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.

15. Calculating Percentages Int 2 Appreciation / Depreciation Appreciation : Going up in value e.g. House value Depreciation : Going down in value e.g. car value

16. Average house prices in Ayr have appreciated by 79% over the past 10 years. If you bought a house for £64995 ten years ago, 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

17. 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

18. 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

19. Calculating Percentages Int 2 Now try MIA Ex 4 Ch2 (page 12) Odd Numbers

20. Int 2 Starter 5cm 6cm

21. 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.

22. 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 2009 a worker received a wage of £300 per week. If inflation is 2% in 2009, what should be his wage be in 2010. 2009 inflation = 2% 2% of £300 = £6 His wage should be £300 + £6 = £306

23. 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%. 2002 inflation = 1.5% 1.5% of £8 = £0.12 Price is £8 + £0.12 = £8.12

24. Calculating Percentages Int 2 Now try MIA Ex 6 Ch2 (page 15)

25. 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.

26. Deduce from question : 100 % - 15 % = 85% 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.

27. Calculating Percentages Int 2 Now try MIA Ex 7 Ch2 (page 17)