1. Compound Interest Amount invested = £3000 Interest Rate = 4% Interest at end of Year 1= 4% of £3000 = 0.04 x £3000 = £120 Amount at end of Year 1= £3120 Interest at end of Year 2= 4% of £3120 = 0.04 x £3120 = £124.80 Amount at end of Year 2= £3120 + £124.80 = £3244.80 and so on Step-by-step Method

2. Amount invested = £3000 Interest Rate = 4% Amount at end of Year 1= 104% of £3000 = 1.04 x £3000= £3120 and so on Using a multiplier Amount at end of Year 2 = 1.04 x £3120 = £3244.80 Try repeated calculations like this one on your calculator Compound Interest

3. Compound Interest – Repeated Calculations £3000 invested at 4% interest End of Year nAmount A(£) 03000.00 1 2 3 4 5 3120.00 3244.80 3374.59 3509.58 3649.96 How much is in the account after 5 years?

4. Amount invested = £3000 Interest Rate = 4% Using indices Amount at end of Year n = 1.04 n x £3000 Amount at end of Year 2 Amount at end of Year 5 = 1.04 2 x £3000 = 1.04 5 x £3000 = £3244.80 = £3649.96 What are the advantages and disadvantages of each method? Compound Interest

5. Depreciation A new car costs £16 000 Age of car (n years)Value (£) 016 000 1 2 3 4 5 13 600 11 560 9826 8352 7099 What will it be worth when it is 5 years old? What will the car be worth when it is 20 years old? Its value falls by 15% per year In this case the multiplier is0.85

6. Falling Sales Formula for annual sales n years from now A company’s sales of a product are falling by 6% per annum. Estimate the annual sales 6 years from now. They sold 45 000 this year. = 0.94 n x 45 000 Estimate of annual sales 6 years from now = 0.94 6 x 45 000 about 31 000 Check this by repeated calculations. In this case the multiplier is 0.94

7. Combining % Changes Number after receiving 3% extra = 103% of 2000 = 1.03 x 2000 A shareholder owns 2000 shares. How many shares will she have after these transactions? She expects to get 3% more shares then plans to sell 25% of her shareholding. = 2060 Number after selling 25%= 75% of 2060 = 0.75 x 2060= 1545 What % is this of her original shareholding? = 77.25% 1545 2000  100 or 1.03 x 0.75 = 0.7725

8. Combining other % Sale Price = 75% of normal price = 75% of 130% of cost price A shop marks up the goods it sells by 30% What is the overall % profit or loss on goods sold in the sale? In a sale it reduces its normal prices by 25% The shop makes a 2.5% loss on goods it sells in the sale = 0.975 of cost price = 0.75 x 1.3 x cost price

9. Reversing % Changes 1.025 x previous price = £66.42 Previous price The price of a train fare increased by 2.5% recently. How much did it cost before the rise in price? It now costs £66.42 Previous price= £64.80 = £66.42  1.025

10. Reversing % Changes 0.875 x full price = £25.90 Full price After a 12.5% discount, the insurance costs £25.90 Full price = £29.60 = £25.90  0.875 What was the cost before the discount?