Compound Interest Amount invested 1000 Interest Rate 5
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Compound Interest Amount invested = £ 1000 Interest Rate = 5% Method 1 Interest at end of Year 1 = 5% of £ 1000 = 0. 05 x £ 1000 Amount at end of Year 1 = £ 50 = £ 1050 Interest at end of Year 2 = 5% of £ 1050 = 0. 05 x £ 1050 Amount at end of Year 2 = £ 52. 50 = £ 1050 + £ 52. 50 = £ 1102. 50 and so on
Compound Interest Amount invested = £ 1000 Interest Rate = 5% Method 2 Amount at end of Year 1 Amount at end of Year 2 = 105% of £ 1000 = 1. 05 x £ 1000 = £ 1050 = 1. 05 x £ 1050 = £ 1102. 50 and so on
Example – Compound Interest £ 1000 invested at 5% interest End of Year n Amount A(£) 0 1000. 00 1 1050. 00 2 1102. 50 3 1157. 63 4 5 1215. 51 1276. 28
Compound Interest Amount invested = £ 1000 Interest Rate = 5% Method 3 Amount at end of Year n = 1. 05 n x £ 1000 Amount at end of Year 2 = 1. 052 x £ 1000 = £ 1102. 50 Amount at end of Year 10 = 1. 0510 x £ 1000 = £ 1628. 89
General Formulae Exponential Growth y = ka mx k, a and m positive a > 1 Example – Compound Interest A = 1. 05 n x £ 1000 y is A x is n k = 1000 a = 1. 05 m = 1 Can be written in other forms: A = 1. 10250. 5 n x £ 1000 k = 1000 a = 1. 1025 m = 0. 5
Example – Radioactive Decay Plutonium has a half-life of 24 thousand years Number of half-lives Time (000 s years) Amount (g) 0 0 1000 1 24 500 2 48 250 3 72 125 4 96 5 120 62. 5 31. 25
Example – Radioactive Decay of Plutonium Decay functions A = 1000 x 0. 5 n where n = no. of half lives A = 1000 x 2 -t/24 where t = time in thousands of years A = 1000 x 2 -0. 0416 t where t = time in thousands of years Exponential Decay y = ka mx k and a positive a < 1 m positive a > 1 m negative
General Shape of Graphs Exponential Growth Exponential Decay
