Compound Interest Amount invested 3000 Interest Rate 4

Compound Interest Amount invested = £ 3000 Interest Rate = 4% Step-by-step Method 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

Compound Interest Amount invested = £ 3000 Interest Rate = 4% Using a multiplier Amount at end of Year 1 = 104% of £ 3000 = 1. 04 x £ 3000 = £ 3120 Amount at end of Year 2 = 1. 04 x £ 3120 = £ 3244. 80 and so on Try repeated calculations like this one on your calculator

Compound Interest – Repeated Calculations £ 3000 invested at 4% interest How much is in the account after 5 years? End of Year n Amount A(£) 0 3000. 00 1 3120. 00 2 3244. 80 3 3374. 59 4 3509. 58 5 3649. 96

Compound Interest 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 = 1. 042 x £ 3000 = £ 3244. 80 Amount at end of Year 5 = 1. 045 x £ 3000 = £ 3649. 96 What are the advantages and disadvantages of each method?

Depreciation A new car costs £ 16 000 Its value falls by 15% per year What will it be worth when it is 5 years old? In this case the multiplier is 0. 85 Age of car (n years) Value (£) 0 16 000 1 13 600 2 11 560 3 9826 4 8352 5 7099 What will the car be worth when it is 20 years old?

Falling Sales A company’s sales of a product are falling by 6% per annum. They sold 45 000 this year. Estimate the annual sales 6 years from now. In this case the multiplier is 0. 94 Formula for annual sales n years from now = 0. 94 n x 45 000 Estimate of annual sales 6 years from now = 0. 946 x 45 000 about 31 000 Check this by repeated calculations.

Combining % Changes A shareholder owns 2000 shares. She expects to get 3% more shares then plans to sell 25% of her shareholding. How many shares will she have after these transactions? Number after receiving 3% extra = 103% of 2000 = 1. 03 x 2000 = 2060 Number after selling 25% = 75% of 2060 = 0. 75 x 2060 = 1545 What % is this of her original shareholding? 1545 2000 100 = 77. 25% or 1. 03 x 0. 75 = 0. 7725

Combining other % A shop marks up the goods it sells by 30% In a sale it reduces its normal prices by 25% What is the overall % profit or loss on goods sold in the sale? Sale Price = 75% of normal price = 75% of 130% of cost price = 0. 75 x 1. 3 x cost price = 0. 975 of cost price The shop makes a 2. 5% loss on goods it sells in the sale

Reversing % Changes The price of a train fare increased by 2. 5% recently. It now costs £ 66. 42 How much did it cost before the rise in price? 1. 025 x previous price = £ 66. 42 Previous price = £ 66. 42 1. 025 Previous price = £ 64. 80

Reversing % Changes After a 12. 5% discount, the insurance costs £ 25. 90 What was the cost before the discount? 0. 875 x full price = £ 25. 90 Full price = £ 25. 90 0. 875 Full price = £ 29. 60